Would you rather have a fish or know how to fish?


Public domain

Jonny Robinson | Aeon Ideas

Imagine the following. You are living a life with enough money and health and time so as to allow an hour or two of careless relaxation, sitting on the sofa at the end of the day in front of a large television, half-heartedly watching a documentary about solar energy with a glass of wine and scrolling through your phone. You happen to hear a fact about climate change, something to do with recent emission figures. Now, on that same night, a friend who is struggling to meet her financial commitments has just arrived at her second job and misses out on the documentary (and the relaxation). Later in the week, when the two of you meet for a drink and your friend is ignorant of recent emission figures, what kind of intellectual or moral superiority is really justified on your part?

This example is designed to show that knowledge of the truth might very well have nothing to do with our own efforts or character. Many are born into severe poverty with a slim chance at a good education, and others grow up in religious or social communities that prohibit certain lines of enquiry. Others still face restrictions because of language, transport, money, sickness, technology, bad luck and so on. The truth, for various reasons, is much harder to access at these times. At the opposite end of the scale, some are effectively handed the truth about some matter as if it were a mint on their pillow, pleasantly materialising and not a big deal. Pride in this mere knowledge of the truth ignores the way in which some people come to possess it without any care or effort, and the way that others strive relentlessly against the odds for it and still miss out. The phrase ‘We know the truth [and, perhaps, you don’t]’, weaponised and presented without any qualifying modesty, fails to recognise the extraordinary privileges so often involved in that very acquisition, drawing an exclusionary line that overlooks almost everything else of significance.

A good attitude towards knowledge shines through various character traits that put us in a healthy relationship with it. Philosophers call these traits epistemic virtues. Instead of praising those people who happen to possess some piece of knowledge, we ought to praise those who have the right attitude towards it, since only this benchmark also includes those who strive for the truth and miss out on it for reasons not entirely under their control. Consider traits such as intellectual humility (a willingness to be wrong), intellectual courage (to pursue truths that make us uncomfortable), open-mindedness (to contemplate all sides of the argument, limiting preconceptions), and curiosity (to be continually seeking). You can see that the person ready to correct herself, courageous in her pursuit of the truth, open-minded in her deliberation, and driven by a deep curiosity has a better relationship to truth even where she occasionally fails to obtain it than does the indifferent person who is occasionally handed the truth on a silver platter.

In a sense, it’s difficult to answer to the disjunction ‘Is it better to know, or to seek to know?’ because there is not quite enough information in it. In respect to knowing (the first half of the disjunction), we also want to hear how that knowledge came about. That is, was the knowledge acquired despite the disinterest and laziness of the possessor, or was it acquired through diligent seeking? If the latter, then it is better to know since the second half of the disjunction is also accommodated in the first: the possession of knowledge and the attitude of seeking it. We can build on the idea with another example.

Would you rather have a fish or know how to fish? Again, we need some more information. If having the fish is the result of knowing how to fish, then once more the two halves of the disjunction are not necessarily mutually exclusive, and this combination is the ideal. But, if the having is the result of waiting around for someone to give you a fish, it would be better to know how to do it yourself. For where the waiting agent hopes for luck or charity, the agent who knows how to fish can return to the river each morning and each evening, throwing her line into the water over and over until she is satisfied with the catch.

And so it is with knowledge. Yes, it’s better to know, but only where this implies an accompanying attitude. If, instead, the possession of knowledge relies primarily upon the sporadic pillars of luck or privilege (as it so often does), one’s position is uncertain and in danger of an unfounded pride (not to mention pride’s own concomitant complications). Split into two discrete categories, then, we should prefer seeking to knowing. As with the agent who knows how to fish, the one who seeks knowledge can go out into the world, sometimes failing and sometimes succeeding, but in any case able to continue until she is satisfied with her catch, a knowledge attained. And then, the next day, she might return to the river and do it all again.

A person will eventually come up against the world, logically, morally, socially, even physically. Some collisions will be barely noticeable, others will be catastrophic. The consistent posture of seeking the truth gives us the best shot at seeing clearly, and that is what we should praise and value.Aeon counter – do not remove

Jonny Robinson is a tutor and casual lecturer in the department of philosophy at Macquarie University. He lives in Sydney.

This article was originally published at Aeon and has been republished under Creative Commons. View the original article here.

What do you really believe?


Portrait of a Man with a Quilted Sleeve, Titian, c1509. Courtesy Wikipedia/National Gallery, London.

Keith Frankish | Aeon Ideas

Edited by Nigel Warburton

Most of us have views on politics, current events, religion, society, morality and sport, and we spend a lot of time expressing these views, whether in conversation or on social media. We argue for our positions, and get annoyed if they are challenged. Why do we do this? The obvious answer is that we believe the views we express (ie, we think they are true), and we want to get others to believe them too, because they are true. We want the truth to prevail. That’s how it seems. But do we really believe everything we say? Are you always trying to establish the truth when you argue, or might there be other motives at work?

These questions might seem strange, offensive even. Am I suggesting that you are insincere or hypocritical in your views? No – at least I’m not suggesting that you are consciously so. But you might be unconsciously influenced by concerns other than truth. Nowadays, most psychologists agree that rapid, unconscious mental processes (sometimes called ‘System 1’ processes) play a huge role in guiding our behaviour. These processes are not thought of as Freudian ones, involving repressed memories and desires, but as ordinary, everyday judgments, motives and feelings that operate without conscious awareness, like a mental autopilot.

It seems plausible that such processes guide much of our speech. After all, we rarely give conscious thought to our reasons for saying what we do; the words just come to our lips. But if the motives behind our words are unconscious, then we must infer them from our behaviour, and might be mistaken about what they are. Again, this isn’t a revolutionary idea; for centuries, dramatists and novelists have depicted people deceived about their own motives. (For more on the nature and limits of self-knowledge, see my earlier Aeon article.)

It’s easy to think of motives that might prompt us to express a view we don’t really believe. We might want it to be true, and feel reassurance when we argue for it (think of the parents who insist that their missing child is still alive, despite the lack of evidence). We might associate it with people we admire, and assert it so as to be like them (think of how people are influenced by the views of celebrities). We might think that it will get us attention, and make us seem interesting (think of teenagers who adopt provocative views). We might profess it to fit in and gain social acceptance (think of a university student from a conservative background). Or we might feel that we have a duty to defend it because of our commitment to some creed or ideology (we sometimes call this attitude faith – belief in the religious sense).

Such motives might also be reinforced by other factors. As a society, we tend to admire people who know their own minds and stick to their principles. So, once we have expressed a view, for whatever reason, we might feel (again, unconsciously) that we are now committed to it, and should stick with it as a matter of integrity. At the same time, we might develop an emotional attachment to the view, a bit like an attachment to a sports team. It is now our view, the one we have publicly endorsed, and we want it to win out over its rivals just because it is ours. In this way, we might come to have a strong personal commitment to a claim, even if we don’t really believe it.

I am not suggesting that we are never guided by concerns for truth and knowledge (what philosophers call epistemic concerns), but I suspect that these sorts of emotional and social factors play a much larger role than we like to think. How else can we explain the vehemence with which people defend their views, and the hurt they feel when their views are challenged?

Is it bad if we sometimes say things we don’t believe? It might seem not. The aims I’ve mentioned – seeking social acceptance, for example, or cultivating a self-image – are not necessarily bad ones, and since they are unconscious it is arguable that we shouldn’t be held responsible for them anyway. There are dangers, however. For in order to achieve these aims we must convince our audience that we genuinely believe what we say. If they thought we were saying something merely in order to create an impression on them, then we wouldn’t succeed in creating that impression. And when our aim is to make some impression on ourselves – like the parents who insist that their child is still alive – we must convince ourselves that we believe it too. As a consequence, we might need to back up our words with deeds, acting as if we believe what we say. If there were a glaring disparity between what we said and did, our insincerity would be obvious. In this way, unconscious desires for acceptance, approval and reassurance can lead us to make choices on the basis of claims for which we have no good evidence, with obvious risks of frustration and failure.

Is there, then, any way of telling whether you really believe a claim? It might seem that conscious reflection would settle it. If you consciously entertain the claim, do you think it is true? Even this process might be unreliable, however. Many theorists hold that conscious thinking is simply talking to oneself in inner speech, in which case it can be guided by unconscious motives, just like outer speech. And, as I mentioned, unconscious desires can prompt us to deceive ourselves, telling ourselves that a claim is true even though we don’t really believe it.

Despite this, a thought experiment might help us detect what we genuinely believe to be true. In real life, there might be few contexts where truth really is our dominant concern: maintaining a comforting view or upholding a cherished ideology or self-image might almost always be more important to us than truth. But suppose you were being questioned by the Truth Demon – a super-powerful being who knows the truth on every topic, and will punish you horribly if you give a wrong answer or fail to answer at all. If you continue to assert a claim when the Truth Demon asks you if it is true, then you do really believe it, really think it is true. But if you give a different answer when under threat of torture by the all-knowing demon, then you don’t really believe the claim. This gives us a practical test for belief: imagine the situation just described as vividly as you can, and see what you would say about any of your views. But do be careful not to give too much conscious thought to the matter in case you start telling yourself what you want to hear.Aeon counter – do not remove

Keith Frankish is an English philosopher and writer. He is a visiting research fellow with the Open University in the UK and an adjunct professor with the Brain and Mind Programme at the University of Crete. He lives in Greece.

This article was originally published at Aeon and has been republished under Creative Commons.


I like the gist of this article (along with the author’s previous article), but the Truth Demon (a.k.a. God) thought experiment could use some work. It’s too easy to deceive and delude oneself, even under imagined duress. It’s also unclear if many people would be “punished horribly” while expressing their false beliefs in good conscience. As mentioned by the author, a good judge of honest belief is one’s actions, but there is a difference between honest belief and truth itself (or is there?). Although the author’s final word is on point, I prefer Nietzsche’s thought experiment: “What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: ‘This life as you now live it and have lived it, you will have to live once more and innumerable times more’ … Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: ‘You are a god and never have I heard anything more divine.”

We don’t know ourselves, we knowledgeable people—we are personally ignorant
about ourselves. And there’s good reason for that. We’ve never tried to find out who
we are. How could it ever happen that one day we’d discover our own selves? With
justice it’s been said that “Where your treasure is, there shall your heart be also.” Our treasure lies where the beehives of our knowledge stand. We are always busy with our knowledge, as if we were born winged creatures—collectors of intellectual honey. In our hearts we are basically concerned with only one thing, to “bring something home.” As far as the rest of life is concerned, what people call “experience”—which of us is serious enough for that? Who has enough time? In these matters, I fear, we’ve been “missing the point.”

Our hearts have not even been engaged—nor, for that matter, have our ears! We’ve
been much more like someone divinely distracted and self-absorbed into whose ear
the clock has just pealed the twelve strokes of noon with all its force and who all at
once wakes up and asks himself “What exactly did that clock strike?”—so we rub
ourselves behind the ears afterwards and ask, totally surprised and embarrassed “What have we really just experienced? And more: “Who are we really?” Then, as I’ve mentioned, we count—after the fact—all the twelve trembling strokes of the clock of our experience, our lives, our being—alas! in the process we keep losing the count. So we remain necessarily strangers to ourselves, we do not understand ourselves, we have to keep ourselves confused. For us this law holds for all eternity: “Each man is furthest from himself.” Where we ourselves are concerned, we are not “knowledgeable people.”

― Friedrich Nietzsche, On the Genealogy of Morals/Ecce Homo

When subjectivity, inwardness, is the truth, the truth becomes objectively determined as a paradox, and that it is paradoxical is made clear by the fact that subjectivity is truth, for it repels objectivity, and the expression for the objective repulsion is the intensity and measure of inwardness. The paradox is the objective uncertainty, which is the expression for the passion of inwardness, which is precisely the truth. This is the Socratic principle. The eternal, essential truth, that is, that which relates itself essentially to the individual because it concerns his existence (all other knowledge is, Socratically speaking, accidental, its degree and scope being indifferent), is a paradox. Nevertheless, the eternal truth is not essentially in itself paradoxical, but it becomes so by relating itself to an existing individual. Socratic ignorance is the expression of this objective uncertainty, the inwardness of the existential subject is the truth. To anticipate what I will develop later, Socratic ignorance is an analogy to the category of the absurd, only that there is still less objective certainty in the absurd, and therefore infinitely greater tension in its inwardness. The Socratic inwardness that involves existence is an analogy to faith, except that this inwardness is repulsed not by ignorance but by the absurd, which is infinitely deeper. Socratically the eternal, essential truth is by no means paradoxical in itself, but only by virtue of its relation to an existing individual.

― Søren Kierkegaard, Concluding Unscientific Postscript

Scientism contra Philosophy

Many people mistake knowledge for wisdom because they are intimately related, and this is unfortunate because they are quite different in an important way. Knowledge is the accumulation of facts and information. Wisdom is the synthesis of knowledge and experiences into insights that deepen one’s understanding of relationships and the meaning of life. In other words, knowledge is a tool, and wisdom is the craft in which the tool is used.

If one understands this difference, he or she will also appreciate why it is vital to properly distinguish between the two. With the Internet, it is now relatively easy for a reasonably diligent person to quickly become knowledgeable in virtually any field of his or her choosing. We are literally awash in a sea of information! But having a hammer and knowing how to use it are two entirely different propositions. A hammer is amoral. Whether it is used for good or ill depends entirely on the wielder. Sadly, history is a lengthy record of the harms wrought by knowledgeable, well-meaning people who lacked wisdom.

In contrast to knowledge, wisdom is generally considered to be morally good. Why is this the case? Albert Einstein once said, ‘Wisdom is not a product of schooling but of the lifelong attempt to acquire it.’ Such a process is lengthy and arduous, which teaches the pursuer patience and humility. Seldom is a person unchanged by such a trial. When one finally uncovers a connection or insight that he or she believes to be universally applicable ‘truth,’ it often inspires awe akin to a spiritual experience.

‘Knowledge comes, but wisdom lingers,’ wrote Alfred, Lord Tennyson. Truths stay with a person for the rest of his or her life, coloring all subsequent thoughts and actions. Wisdom requires no law or threat of punishment to ensure compliance. The practitioner typically feels a strong compulsion to obey his or her own beliefs. The wise can still fall prey to indiscretions and questionable moral behavior–being flesh and blood like us all–however, if one tracks such statistics, the odds of such failings are likely to be very small compared to the general populace.

Society esteems the wise for their virtuosity and for their rarity. Subject matter experts number in the thousands, but the wise may only number in the tens or hundreds. And history records their names and achievements for posterity’s sake.

. . . . .

This critical insight is brought to you by Justarius of Philoscifi.com

If scientific method is only one form of a general method employed in all human inquiry, how is it that the results of science are more reliable than what is provided by these other forms? I think the answer is that science deals with highly quantified variables and that it is the precision of its results that supplies this reliability. But make no mistake: Quantified precision is not to be confused with a superior method of thinking.

– James Blachowicz, The New York Times

See Also

Hawking contra Philosophy

We Know So Little About So Much

I find it very interesting that even with the exponential growth in knowledge that we have witnessed from ancient times through the industrial age to the digital age, there still remains so much that is simply unknown to us. I have no doubt that the human spirit will in time conquer each and every question that it poses to itself. The following is a list of unsolved problems in various fields of scientific and philosophical inquiry. Aside from the solutions being interesting in themselves and offering the opportunity of contributing to our collective history, some of these problems even offer monetary incentives for proven solutions. So go ahead and tackle one!

We know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power.

– Bertrand Russell

Unsolved Problems in Artificial Intelligence

In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems is equivalent to that of solving the central artificial intelligence problem—making computers as intelligent as people, or strong AI.[1] To call a problem AI-complete reflects an attitude that it would not be solved by a simple specific algorithm.

AI-complete problems are hypothesised to include computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real world problem.[2]

Currently, AI-complete problems cannot be solved with modern computer technology alone, but would also require human computation. This property can be useful, for instance to test for the presence of humans as with CAPTCHAs, and for computer security to circumvent brute-force attacks.[3][4]


The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous class of difficult problems.[5] Early uses of the term are in Erik Mueller’s 1987 Ph.D. dissertation[6] and in Eric Raymond‘s 1991 Jargon File.[7]

AI-complete problems

AI-complete problems are hypothesised to include:

Machine translation

Main article: Machine translation

To translate accurately, a machine must be able to understand the text. It must be able to follow the author’s argument, so it must have some ability to reason. It must have extensive world knowledge so that it knows what is being discussed — it must at least be familiar with all the same commonsense facts that the average human translator knows. Some of this knowledge is in the form of facts that can be explicitly represented, but some knowledge is unconscious and closely tied to the human body: for example, the machine may need to understand how an ocean makes one feel to accurately translate a specific metaphor in the text. It must also model the authors’ goals, intentions, and emotional states to accurately reproduce them in a new language. In short, the machine is required to have wide variety of human intellectual skills, including reason, commonsense knowledge and the intuitions that underlie motion and manipulation, perception, and social intelligence.Machine translation, therefore, is believed to be AI-complete: it may require strong AI to be done as well as humans can do it.

Software brittleness

Main article: Software brittleness

Current AI systems can solve very simple restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempt to “scale up” their systems to handle more complicated, real world situations, the programs tend to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they fail as unexpected circumstances outside of its original problem context begin to appear. When human beings are dealing with new situations in the world, they are helped immensely by the fact that they know what to expect: they know what all things around them are, why they are there, what they are likely to do and so on. They can recognize unusual situations and adjust accordingly. A machine without strong AI has no other skills to fall back on.[8]


Computational complexity theory deals with the relative computational difficulty of computable functions. By definition it does not cover problems whose solution is unknown or has not been characterised formally. Since many AI problems have no formalisation yet, conventional complexity theory does not allow the definition of AI-completeness.

To address this problem, a complexity theory for AI has been proposed.[9] It is based on a model of computation that splits the computational burden between a computer and a human: one part is solved by computer and the other part solved by human. This is formalised by a human-assisted Turing machine. The formalisation defines algorithm complexity, problem complexity and reducibility which in turn allows equivalence classes to be defined.

The complexity of executing an algorithm with a human-assisted Turing machine is given by a pair \langle\Phi_{H},\Phi_{M}\rangle, where the first element represents the complexity of the human’s part and the second element is the complexity of the machine’s part.


The complexity of solving the following problems with a human-assisted Turing machine is:[9]

  • Optical character recognition for printed text: \langle O(1), poly(n) \rangle
  • Turing test:
    • for an n-sentence conversation where the oracle remembers the conversation history (persistent oracle): \langle O(n), O(n) \rangle
    • for an n-sentence conversation where the conversation history must be retransmitted: \langle O(n), O(n^2) \rangle
    • for an n-sentence conversation where the conversation history must be retransmitted and the person takes linear time to read the query: \langle O(n^2), O(n^2) \rangle
  • ESP game: \langle O(n), O(n) \rangle
  • Image labelling (based on the Arthur–Merlin protocol): \langle O(n), O(n) \rangle
  • Image classification: human only: \langle O(n), O(n) \rangle , and with less reliance on the human: \langle O(\log n), O(n \log n) \rangle .

See also


  1. Jump up^ Shapiro, Stuart C. (1992). Artificial Intelligence In Stuart C. Shapiro (Ed.), Encyclopedia of Artificial Intelligence (Second Edition, pp. 54–57). New York: John Wiley. (Section 4 is on “AI-Complete Tasks”.)
  2. Jump up^ Roman V. Yampolskiy. Turing Test as a Defining Feature of AI-Completeness . In Artificial Intelligence, Evolutionary Computation and Metaheuristics (AIECM) –In the footsteps of Alan Turing. Xin-She Yang (Ed.). pp. 3-17. (Chapter 1). Springer, London. 2013. http://cecs.louisville.edu/ry/TuringTestasaDefiningFeature04270003.pdf
  3. Jump up^ Luis von Ahn, Manuel Blum, Nicholas Hopper, and John Langford. CAPTCHA: Using Hard AI Problems for Security. In Proceedings of Eurocrypt, Vol. 2656 (2003), pp. 294-311.
  4. Jump up^ Bergmair, Richard (January 7, 2006). “Natural Language Steganography and an “AI-complete” Security Primitive”. CiteSeerX: (unpublished?)
  5. Jump up^ Mallery, John C. (1988), “Thinking About Foreign Policy: Finding an Appropriate Role for Artificially Intelligent Computers”, The 1988 Annual Meeting of the International Studies Association., St. Louis, MO.
  6. Jump up^ Mueller, Erik T. (1987, March). Daydreaming and Computation (Technical Report CSD-870017) Ph.D. dissertation, University of California, Los Angeles. (“Daydreaming is but one more AI-complete problem: if we could solve any one artificial intelligence problem, we could solve all the others”, p. 302)
  7. Jump up^ Raymond, Eric S. (1991, March 22). Jargon File Version 2.8.1 (Definition of “AI-complete” first added to jargon file.)
  8. Jump up^ Lenat, Douglas; Guha, R. V. (1989), Building Large Knowledge-Based Systems, Addison-Wesley, pp. 1–5
  9. ^ Jump up to:a b Dafna Shahaf and Eyal Amir (2007) Towards a theory of AI completeness. Commonsense 2007, 8th International Symposium on Logical Formalizations of Commonsense Reasoning.

Unsolved Problems in Biology

Adaptation At present there is no theoretical model for how adaptation occurs that is close to being complete. Mathematical models of evolution (e.g. within population genetics) describe how the process of natural selection influences the frequency of already-existing gene variants based on their relative fitnesses. Only a small amount of theory treats the problem of modelling the generation of new variants through mutation, in terms of either the fitnesses or phenotypic forms they confer.
Alkaloids The function of these substances in living organisms which produce them is not known[1]
Arthropod head problem A long-standing zoological dispute concerning the segmental composition of the heads of the various arthropod groups, and how they are evolutionarily related to each other.
Basking shark Only the right ovary in this fish appears to function, the reason is unknown.
Biological aging There are a number of hypotheses why senescence occurs including those that it is programmed by gene expression changes and that it is the accumulative damage of biological processes.
Blue Whale There is not much data on the sexuality of the biggest animal ever.[2]
Botany/Plants What is the exact evolutionary history of flowers and their blossoms?
Butterfly migration How do the descendants of Monarch butterfly all over Canada and the US eventually, after migrating for several generations, manage to return to a few relatively small overwintering spots?
Cambrian explosion What is the cause of the apparent rapid diversification of multicellular animal life around the beginning of the Cambrian, resulting in the emergence of almost all modern animal phyla?
Consciousness What is the brain basis of subjective experience, cognition, wakefulness, alertness, arousal, and attention? Is there a “hard problem of consciousness“? If so, how is it solved? What, if any, is the function of consciousness?[3][4]
Evolution of sex What selective advantages drove the development of sexual reproduction, and how did it develop?[5]
Extraterrestrial life Might life which does not originate from planet Earth also have developed on other planets? Might this life be intelligent?
Gall wasp It is largely unknown how these insects induce gall formation in plants; chemical, mechanical, and viral triggers have been discussed.
Glycogen body The function of this structure is not known.
Golgi apparatus In cell theory, what is the exact transport mechanism by which proteins travel through the Golgi apparatus?
Hammerhead shark The reason for their distinctive and unusual head structure is not known.
Homing (biology) A satisfactory explanation for the neurobiological mechanisms that allow Homing, has yet to be found.
Korarchaeota Their metabolic processes are so far unclear.
Latitudinal diversity gradient Why does biodiversity increase when going from the poles towards the equator?
Loricifera There are at least 100 species of this phylum that are yet to be described, but none of them is known to be present in the fossil record.
Origin of life Exactly how and when did life on Earth originate? Which, if any, of the many hypotheses is correct?
Paradox of the plankton The high diversity of phytoplankton seems to violate the competitive exclusion principle.


  1. Jump up^ Aniszewski, p. 142
  2. Jump up^ Articleworld.org Blue Whale
  3. Jump up^ Sejnowski, Terrence J.; Hemmen, J. L. van (2006). 23 problems in systems neuroscience (PDF). Oxford [Oxfordshire]: Oxford University Press. ISBN 0-19-514822-3.
  4. Jump up^ Tononi, G; Koch, C. (2015). “Consciousness: Here, there and everywhere?” (PDF). Philosophical Transactions of the Royal Society London B.
  5. Jump up^ Thomas N. Sherratt, David M. Wilkinson. Big questions in ecology and evolution. Oxford University Press US, 2009. ISBN 978-0-19-954861-3

Unsolved Problems in Chemistry

Unsolved problems in chemistry tend to be questions of the kind “Can we make X chemical compound?”, “Can we analyse it?”, “Can we purify it?” and are commonly solved rather quickly, but may just as well require considerable efforts to be solved. However, there are also some questions with deeper implications. This article tends to deal with the areas that are the center of new scientific research in chemistry. Problems in chemistry are considered unsolved when an expert in the field considers it unsolved or when several experts in the field disagree about a solution to a problem.

Physical chemistry problems

Organic chemistry problems

In addition to these, it is noteworthy that many mechanisms proposed for catalytic processes are poorly understood[which?] and often fail to explain all relevant phenomena.[citation needed]

Biochemistry problems

  • Enzyme kinetics: Why do some enzymes exhibit faster-than-diffusion kinetics?[8]
  • Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?[5][9] This has been achieved for several small globular proteins in recent years.[10]
  • RNA folding problem: Is it possible to accurately predict the secondary, tertiary and quaternary structure of a polyribonucleic acid sequence based on its sequence and environment?
  • What are the chemical origins of life? How did non-living chemical compounds generate self-replicating, complex life forms?
  • Protein design: Is it possible to design highly active enzymes de novo for any desired reaction?[11]
  • Biosynthesis: Can desired molecules, natural products or otherwise, be produced in high yield through biosynthetic pathway manipulation?[12]


  1. ^ Jump up to:a b c The Future of Post-Human Chemistry: A Preface to a New Theory of Substances …, de Peter Baofu, page 285
  2. Jump up^ The problem may actually occur at approximately Element 173, given the finite extension of nuclear-charge distribution.[citation needed] See the article on Extension of the periodic table beyond the seventh period, and the article section Relativistic effects of Atomic orbital.
  3. Jump up^ Duffie, John A. (August 2006). Solar Engineering of Thermal Processes. Wiley-Interscience. p. 928. ISBN 978-0-471-69867-8.
  4. Jump up^ Brabec, Christoph; Vladimir Dyakonov; Jürgen Parisi; Niyazi Serdar Sarıçiftçi (March 2006). Organic Photovoltaics: Concepts and Realization. Springer. p. 300. ISBN 978-3-540-00405-9.
  5. ^ Jump up to:a b “So much more to know”. Science 309 (5731): 78–102. July 2005. doi:10.1126/science.309.5731.78b. PMID 15994524.
  6. Jump up^ S. Narayan, J. Muldoon, M.G. Finn, V.V. Fokin, H.C. Kolb, K.B. Sharpless,2005, “On Water: Unique Reactivity of Organic Compounds in Aqueous Suspension,” Angew. Chem. Int. Ed. 21:3157, see [onlinelibrary.wiley.com/doi/10.1002/anie.200462883/full]. accessed 15 December 2015.
  7. Jump up^ Fredrik von Kieseritzky, 2013, “What is the true nature of gold-sulfur bonds?”, see [1], accessed 15 December 2014.
  8. Jump up^ Hsieh M, Brenowitz M (August 1997). “Comparison of the DNA association kinetics of the Lac repressor tetramer, its dimeric mutant LacIadi, and the native dimeric Gal repressor”. J. Biol. Chem. 272 (35): 22092–6. doi:10.1074/jbc.272.35.22092. PMID 9268351.
  9. Jump up^ King, Jonathan (2007). “MIT OpenCourseWare – 7.88J / 5.48J / 7.24J / 10.543J Protein Folding Problem, Fall 2007 Lecture Notes – 1”. MIT OpenCourseWare. RetrievedJune 22, 2013.
  10. Jump up^ Dill KA; et al. (June 2008). “The Protein Folding Problem”. Annu Rev Biophys 37: 289–316. doi:10.1146/annurev.biophys.37.092707.153558. PMID 9268351.
  11. Jump up^ http://depts.washington.edu/bakerpg/drupal/node/465
  12. Jump up^ http://www.nature.com/nature/journal/v488/n7411/full/nature11478.html

External links

Unsolved Problems in Computer Science

This article is a list of unsolved problems in computer science. A problem in computer science is considered unsolved when an expert in the field (i.e, a computer scientist) considers it unsolved or when several experts in the field disagree about a solution to a problem.

Computational complexity


Programming language theory

Other problems

External links

Unsolved Problems in Economics

This is a list of some of the major unsolved problems, puzzles, or questions in neoclassical economics. Some of these are theoretical in origin and some of them concern the inability of orthodox economic theory to explain an empirical observation.

Behavioral economics

Main article: Behavioral economics
  • Revealed preference: Does Revealed Preference theory truly reveal consumer preference when the consumer is able to afford all of the available options? For example, if a consumer is confronted with three goods and they can afford to purchase all three (A, B, and C) and they choose to first purchase A, then C, and then B – does this suggest that the consumer preference for the goods is A > C > B? The debate rests on the fact that since the consumer can afford all three goods and does not need to make a preferential decision, does the order of consumption reflect any preference?[1]
  • Tâtonnement: The act of tâtonnement plays a key role in the formulation of general equilibrium theory. The claim is that if an initial contract does not lead to an equilibrium, it is ended and new contracts are formulated. If the initial contract is not called off, it will likely lead to a different set of prices, depending on the degree of error in the original process. The question is whether successive re-contracting continues with the parties forgetting the previously planned positions taken or whether the parties engage in a form of tâtonnement to achieve optimality.[1] See also Hill climbing and Walrasian auction.
  • Unified Models of Human Biases: Neoclassical economics has concentrated on the development of models that reflect an idealized economic agent, sometimes referred to as Homo economicus, as a way of studying economics. In the period spanning the 1970s to the 1990s, research began to emerge that suggested that people were subject to cognitive biases such as the framing effect, loss aversion, the gambler’s fallacy, confirmation bias, and many others. Further, these effects could produce anomalies such as herd behavior or momentum investing inconsistent with economic models that did not incorporate human psychological limitations.[2] While some models have begun to include bounded rationality and risk aversion, such as Prospect Theory, there still remains to be seen a unified model that can make useful predictions that incorporates the entirety of cognitive biases and rational limitations in most humans.[3] Further, there even exists debate as to whether it is necessary to incorporate such psychological limitations into economic models. While some economists insist they are necessary to fully appreciate the complexity of the market, others still contend that a model that incorporates human biases is either unrealistic or question its usefulness arguing that a model that doesn’t approximate agents as being perfectly rational, with the possibility of minimal exceptions, is unlikely to be successful.[3][4]

Financial economics

Main article: Financial economics
  • Equity premium puzzle: The equity premium puzzle is thought to be one of the most important outstanding questions in neoclassical economics.[5] It is founded on the basis that over the last one hundred years or so the average real return to stocks in the US has been substantially higher than that of bonds. The puzzle lies in the explaining the causes behind this equity premium. While there are a number of different theories regarding the puzzle, there still exists no definitive agreement on its cause.[6]
  • Dividend puzzle: The dividend puzzle is the empirically observed phenomenon that companies that pay dividends tend to be rewarded by investors with highervaluations. At present, there is no explanation widely accepted by economists.[7][8][9] The Modigliani-Miller theorem suggests that the puzzle can (only) be explained by some combination of taxes, bankruptcy costs, market inefficiency (including that due to investor psychology), and asymmetric information.
  • Improved Black–Scholes and Binomial Options Pricing models: The Black–Scholes model and the more general binomial options pricing models are a collection of equations that seek to model and price equity and call options. While the models are widely used, they have many significant limitations.[10] Chief among them are the model’s inability to account for historical market movements[11] and their frequent overpricing of options, with the overpricing increasing with the time to maturity.[12] The development of a model that can properly account for the pricing of call options on an asset with stochastic volatility is considered an open problem in financial economics.[12]
  • Problems with the American option: Is there a closed form for American put options? Is there a forward partial differential equation for the American Option in a local volatility model?

International economics

  • Home bias in trade puzzle: The home bias in trade puzzle is an empirical observation that even when factors such as economic size of trading partners and the distance between them are considered, trade between regions within a given country is substantially greater than trade between regions in different countries, even when there are no substantial legal barriers. There is currently no framework to explain this observation.[13][14]
  • Equity home bias puzzle: This puzzle concerns the observation that individuals and institutions in many countries only hold modest amounts of foreign equity, despite the ability for vast diversification of their portfolios in the global economy.[13] While some explanations do exist, such as that local individuals and firms have greater access to information about local firms and economic conditions, these explanations are not accepted by the majority of economists and have been mostly refuted.[15]
  • Backus-Kehoe-Kydland puzzle: The Backus-Kehoe-Kydland consumption correlation puzzle is the empirical observation that consumption is much less correlated across countries than output.[13] Standard economic theory suggests that country-specific output risks should be collective and domestic consumption growth should not depend strongly on country-specific income shocks. Thus, we should not see the observation that consumption is much less correlated across countries than output; and yet we do.[16][17]
  • Feldstein-Horioka puzzle: The Feldstein-Horioka puzzle originates from an article in the 1980s that found that among OECD countries, averages of long-term national savings rates are highly correlated with similar averages of domestic investment rates. Standard economic theory suggests that in relatively open international financial markets, the savings of any country would flow to countries with the most productive investment opportunities; hence, saving rates and domestic investment rates would be uncorrelated, contrary to the empirical evidence suggested by Martin Feldstein and Charles Horioka. While numerous articles regarding the puzzle have been published, none of the explanations put forth have adequate empirical support.[13]
  • PPP Puzzle: The PPP puzzle, considered one of the two real exchange rate puzzles, concerns the observation that real exchange rates are both more volatileand more persistent than most models would suggest. The only clear way to understand this volatility would be to assign substantial roles to monetary and financial shocks. However, if shocks play such a large role the challenge becomes finding what source, if one even exists, of nominal rigidity that could be so persistent to explain the long-term prolonged nature of real exchange rate deviations.[13]
  • The Exchange Rate Disconnect Puzzle: The exchange rate disconnect puzzle, also one of the so-called real exchange rate puzzles, concerns the weak short-term feedback link between exchange rates and the rest of the economy. In most economies, the exchange rate is the most important relative price, so it is surprising, and thus far unexplained entirely, that the correlations are not stronger.[13]


  1. ^ Jump up to:a b Oskar Morgenstern (1972). “Thirteen critical points in contemporary economic theory”. Journal of Economic Literature 10: 1163–1189. JSTOR 2721542.
  2. Jump up^ “Foundations of Behavioral and Experimental Economics: Daniel Kahneman and Vernon Smith” (PDF) (Press release). The Royal Swedish Academy of Sciences. 17 December 2002.
  3. ^ Jump up to:a b Machina, Mark (1987). “Choice under Uncertainty: Problems Solved and Unsolved” (PDF). Journal of Economic Perspectives 1 (1): 121–154. doi:10.1257/jep.1.1.121.
  4. Jump up^ Krugman, Paul (2 September 2009), “How Did Economists Get It So Wrong?”, The New York Times
  5. Jump up^ “Has Barro solved the equity premium puzzle?”. New Economist weblog. 2005-09-29.
  6. Jump up^ Narayana R. Kocherlakota (March 1996). “The Equity Premium: It’s Still a Puzzle” (PDF). Journal of Economic Literature 34: 42–71.
  7. Jump up^ Borges, Maria Rosa (July 2008), Is The Dividend Puzzle Solved ? (PDF)
  8. Jump up^ Prast, Henriette (March 2004), Investor psychology: a behavioral explanation of six finance puzzles (PDF)
  9. Jump up^ Bernheim, B. Douglas (1991). “Tax Policy and the Dividend Puzzle”. RAND Journal of Economics 22 (4): 455–476. doi:10.2307/2600982.
  10. Jump up^ http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-In-defence-of-Black-Scholes-and-Merton
  11. Jump up^ Baggett, L. Scott; Thompson, James; Williams, Edward; Wojciechowski, William (October 2006). “Nobels for nonsense”. Journal of Post Keynesian Economics 29 (1): 3–18.doi:10.2753/pke0160-3477290101.
  12. ^ Jump up to:a b Hull, John; White, Alan (June 1987). “The Pricing of Options on Assets with Stochastic Volatilities”. Journal of Finance 42 (2): 281–300. doi:10.1111/j.1540-6261.1987.tb02568.x.
  13. ^ Jump up to:a b c d e f Obstfeld, Maurice; Rogoff, Kenneth (2000), “The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?”, in Bernanke, Ben; Rogoff, Kenneth, NBER Macroeconomics Annual 2000 15, The MIT Press, pp. 339–390, ISBN 0-262-02503-5
  14. Jump up^ Edmond, Chris, Note 8a from course 316–632 “International Monetary Economics” (PDF) (Handout)
  15. Jump up^ Van Nieuwerburgh, Stijn; Veldkamp, Laura (July 2005). “Information Immobility and the Home Bias Puzzle”. NYU Working Paper. FIN-04-026. ssrn 1294476.
  16. Jump up^ Backus, David K.; Kehoe, Patrick J.; Kydland, Finn E. (1992), “International Real Business Cycles”, Journal of Political Economy 100: 745–775, doi:10.1086/261838
  17. Jump up^ Backus, David K.; Kehoe, Patrick J.; Kydland, Finn E. (1995), “International Business Cycles: Theory and Evidence”, in Cooley, Tom, Frontiers of Business Cycle Research,Princeton University Press, ISBN 0-691-04323-X

Further reading

Unsolved Problems in Geoscience

This article discusses currently unsolved problems in geoscience.

The early Earth and the solar system

  • How did Earth and other planets form? Were planets formed in situ? Or are orbital changes relatively frequent? What determined the different deep layering of the solar planets?[1]
  • Was there ever a collision of the Earth with another planet Theia, giving birth to our satellite?[2] There is compelling evidence, such as measures of a shorter duration of the Earth’s rotation and lunar month in the past, pointing to a Moon much closer to Earth during the early stages of the Solar System.[3]
  • What is the long-term heat balance of Earth? How did its internal temperature decay since it formed by accretion of chondrites? How abundant are radiogenic elements in the interior? Did a “faint young Sun” ever warm a “snowball Earth“? [4][5]
  • What made plate tectonics a dominant process only on Earth?[6] How did the planet cool down before plate tectonics?[7] Was the Earth’s crust formed during the early stages of its evolution or is it the result of a gradual distillation of the mantle that continues today along with crustal recycling? Is the crust still growing or does its recycling compensate for crust formation at mid-ocean ridges and other volcanic areas?

Topography and environment

  • Can the now widely available topographic data be used to derive past tectonic and climatic conditions (in the multi-million year scale)? Do we know enough about the erosion and transport processes? Does the stocasticity of meteorological and tectonic events reflect in the landscape? How much has life contributed to shape the Earth’s surface?
  • Can classical geomorphological concepts such as peneplanation or retrogressive erosion be quantitatively understood? Old mountain ranges such as the Appalachian or the Urals seem to retain relief for >108 years, while subglacial fluvial valleys under Antarctica are preserved under moving ice of kilometric thickness since the Neogene. What controls the time-scale of topographic decay?[8]
  • What are the erosion and transport laws governing the evolution of the Earth’s Surface?[Willenbring et al., Geology, 2013] Rivers transport sediment particles that are at the same time the tools for erosion but also the shield protecting the bedrock. How important is this double role of sediment for the evolution of landscapes?[9][10]
  • How resilient is the ocean to chemical perturbations?
  • What caused the huge salt deposition in the Mediterranean known as the Messinian salinity crisis? Was the Mediterranean truly desiccated? What were the effects on climate and biology, and what can we learn from extreme salt giants like this? How were the normal marine conditions reestablished?[11][12][13][14]
  • There are several places where water does drain or has drained underground, but the destination is unknown. One example is “the Devil’s Kettle” in Minnesota, a pothole which swallows half of the Brule River.[15]

External links


  1. Jump up^ McKinnon, W. B. (12 April 2012). “The Strangest Terrestrial Planet”. Science 336 (6078): 162–163. doi:10.1126/science.1220825.
  2. Jump up^ Canup, R. M. (17 October 2012). “Forming a Moon with an Earth-like Composition via a Giant Impact”. Science 338 (6110): 1052–1055. doi:10.1126/science.1226073.
  3. Jump up^ George, Williams (1991). “Upper Proterozoic Tidal Rhythmites, South Australia: Sedimentary Features, Deposition, and Implications for the Earth’s Paleorotation”. Clastic Tidal Sedimentology – Memoir 16, 1991 (CSPG Special Publications): 161–177. Retrieved 3 March 2015.
  4. Jump up^ Wired: Was the Earth a migratory planet?
  5. Jump up^ Marty, B.; Zimmermann, L.; Pujol, M.; Burgess, R.; Philippot, P. (19 September 2013). “Nitrogen Isotopic Composition and Density of the Archean Atmosphere”. Science 342(6154): 101–104. doi:10.1126/science.1240971.
  6. Jump up^ Martin, Paula; Hunen, Jeroen van; Parman, Stephen; Davidson, Jon (1 March 2008). “Why does plate tectonics occur only on Earth?” (PDF). Physics Education 43 (2): 144–150. doi:10.1088/0031-9120/43/2/002. Retrieved 3 March 2015.
  7. Jump up^ Moore, William B.; Webb, A. Alexander G. (25 September 2013). “Heat-pipe Earth”. Nature 501 (7468): 501–505. doi:10.1038/nature12473. Retrieved 3 March 2015.
  8. Jump up^ Egholm, David L.; Knudsen, Mads F.; Sandiford, Mike (26 June 2013). “Lifespan of mountain ranges scaled by feedbacks between landsliding and erosion by rivers”. Nature498 (7455): 475–478. doi:10.1038/nature12218.
  9. Jump up^ Sklar, Leonard S.; Dietrich, William E. (2001). “Sediment and rock strength controls on river incision into bedrock” (PDF). Geology 29 (12): 1087. doi:10.1130/0091-7613(2001)029<1087:SARSCO>2.0.CO;2. Retrieved 3 March 2015. (effect description and tools)
  10. Jump up^ Cowie, Patience A.; Whittaker, Alexander C.; Attal, Mikaël; Roberts, Gerald; Tucker, Greg E.; Ganas, Athanassios (2008). “New constraints on sediment-flux–dependent river incision: Implications for extracting tectonic signals from river profiles” (PDF). Geology 36 (7): 535. doi:10.1130/G24681A.1. Retrieved 3 March 2015.(field example)
  11. Jump up^ Garcia-Castellanos, D.; Villaseñor, A. (14 December 2011). “Messinian salinity crisis regulated by competing tectonics and erosion at the Gibraltar arc”. Nature 480 (7377): 359–363. doi:10.1038/nature10651. PMID 22170684. Retrieved 3 March 2015. Author Publications Link
  12. Jump up^ Hsü, Kenneth J. (1987). The Mediterranean was a desert : a voyage of the Glomar Challenger (First Princeton paperback printing ed.). Princeton, N.J.: Princeton University Press. ISBN 978-0691024066.
  13. Jump up^ Clauzon, Georges; Suc, Jean-Pierre; Gautier, François; Berger, André; Loutre, Marie-France (1996). “Alternate interpretation of the Messinian salinity crisis: Controversy resolved?”. Geology 24 (4): 363. doi:10.1130/0091-7613(1996)024<0363:AIOTMS>2.3.CO;2.
  14. Jump up^ Krijgsman, W.; Hilgen, F. J.; Raffi, I.; Sierro, F. J.; Wilson, D. S. (12 August 1999). “Chronology, causes and progression of the Messinian salinity crisis”. Nature 400 (6745): 652–655. doi:10.1038/23231.
  15. Jump up^ http://www.mnn.com/earth-matters/wilderness-resources/stories/7-bizarre-places-on-earth-where-water-disappears

Unsolved Problems in Information Theory

This article lists some unsolved problems in information theory which are separated into source coding and channel coding. There are also related unsolved problems[1] in philosophy.

Channel coding

  • Capacity of a network:[2] The capacity of a general wireless network is not known. There are some specific cases for which the capacity is known, such as theAWGN channel and fading channel.
  • Capacity of the broadcast channel:[3][4] The capacity of the broadcast channel, or the case in which a single transmitter is sending information to many receivers is unknown in general, though it is known for several specific cases.
  • Capacity of the interference channel (Two User): The capacity of the interference channel, in the case where there are two transmitter and receiver pairs that interfere among each other, is unknown in general. Capacity is known in special cases: strong interference regime, injective-deterministic. Capacity is known in approximate sense or with in a gap for: injective-semi-deterministic, additive white Gaussian noise with per block power constraint.
  • Capacity of the two-way channel.[5][6] The capacity of the two-way channel (a channel in which information is sent in both directions simultaneously) is unknown.
  • The capacity of Aloha:[7] The ALOHAnet used a very simple access scheme for which the capacity is still unknown, though it is known in a few special cases.
  • Quantum capacity: The capacity of a quantum channel is in general not known.[8]

There are many other unsolved problems in coding theory:[9] and in other areas.[10][11]

Source coding

Distributed source coding: The best way to compress multiple correlated information sources that do not communicate with each other is not known.


  1. Jump up^ Adriaans, Pieter. “Open Problems in the Study of Information and Computation”. Retrieved 21 June 2013.
  2. Jump up^ Cover, Thomas. Elements of Information Theory. Wiley-Interscience. ISBN 978-0471062592.
  3. Jump up^ Cover, Thomas (Oct 1998). “Comments on Broadcast Channels”. IEEE Trans Inf Theory 44 (6): 2524.
  4. Jump up^ Sridharan, Arvind. “Broadcast Channels” (PDF). Notre Dame. Retrieved 6 July 2014.
  5. Jump up^ Shannon, Claude (1961). “Two-way communication channels”. Proc Fourth Berkeley sump on Mathematical Statistics and Probability 1: 611.
  6. Jump up^ meeuwissen, Erik (16 Aug 1998). “The Origin of Two-Way Channels”. Proc ISIT I: 185.
  7. Jump up^ Medard, Muriel (March 2004). “Capacity of Time-Slotted ALOHA Packetized Multiple-Access Systems Over the AWGN Channel” (PDF). EEE Transactions on Wireless COMMUNICATIONS 3 (2). Retrieved 11 July 2014.
  8. Jump up^ Shor, Peter (2000). “Quantum Information Theory: Results and Open Problems” (PDF). Geom. Funct. Anal.: 816–838.
  9. Jump up^ David Joyner; Jon-Lark Kim (2010). Selected Unsolved Problems in Coding Theory. New York: Springer.
  10. Jump up^ Longo, Giuseppe (1975). Information theory: new trends and open problems.
  11. Jump up^ Tse, David (1996). “It’s Easier to Approximate” (PDF). Information Theory Society Newsletter. Retrieved 26 June 2013.

Unsolved Problems in Linguistics

Some of the issues below are commonly recognized as unsolved problems; i.e. it is generally agreed that no solution is known. Others may be described as controversies; i.e. although there is no common agreement about the answer, there are established schools of thought that believe they have a correct answer.


  • Is there a universal definition of word?
  • Is there a universal definition of sentence?
  • Are there any universal grammatical categories?
  • Can the elements contained in words (morphemes) and the elements contained in sentences (syntactic constituents) be shown to follow the same principles?
  • How are domains for phonological processes related to syntactic structure? Do prosodic domains deviate fromsyntactic constituent structure?
  • Is it possible to formally delineate languages from each other? That is to say, is it possible to use linguistic (rather than social) criteria to draw a clear boundary between two closely related languages with a dialect continuumbetween their respective standard forms (e.g. Occitan and Catalan)?
  • How does grammaticalization function?
  • What constitutes grammatically correct language, as viewed by native speakers of that particular language, i.e. the problem of gradient well-formedness)?
  • How do creole languages emerge?
  • How does lexical substitution function given the potentially limitless number of different contexts, the limits of one’s knowledge and the limits of one’s understanding and usage of language?
  • How do idiolects and dialects emerge? Are there any common patterns in their development? Can they be quantitatively and qualitatively measured at all and if so, how?

Philosophy of language



  • Language emergence:
  • Language acquisition:
    • Controversy: infant language acquisition / first language acquisition. How are infants able to learn language? One line of debate is between two points of view: that of psychological nativism, i.e., the language ability is somehow “hardwired” in the human brain, and that of the tabula rasa or blank slate, i.e., language is acquired due to brain’s interaction with environment. Another formulation of this controversy is “nature versus nurture“.
    • Is the human ability to use syntax based on innate mental structures or is syntactic speech the function of intelligence and interaction with other humans? The question is closely related to those of language emergence and acquisition.
    • The language acquisition device: How localized is language in the brain? Is there a particular area in the brain responsible for the development of language abilities or is it only partially localized?
    • What fundamental reasons explain why ultimate attainment in second language acquisition is typically some way short of the native speaker‘s ability, with learners varying widely in performance?
    • What are the optimal ways to achieve successful second-language acquisition?
    • Animals and language: How much language (e.g. syntax) can animals be taught to use? How much of animal communication can be said to have the same properties as human language (e.g. syntax)?
    • What role does linguistic intuition play, how is it formed and how does it function? Is it closely linked to exposure to a unique set of different experiences and their contexts throughout one’s personal life?


Main article: Sociolinguistics

Computational linguistics

  • Is perfect computational word-sense disambiguation attainable by using software? If yes, how and why? If no, why? (This presupposes the solution to the unsolved problems in the other areas of linguistics as a basis.)
  • Is accurate computational word-sense induction feasible? If yes, how and why? If not, why?

Lexicology and lexicography

Main articles: Lexicology and lexicography



  1. Jump up^ Givon, Talmy; Bertram F. Malle (2002). The Evolution of Language Out of Pre-language. John Benjamins. ISBN 1-58811-237-3.
  2. Jump up^ Deacon, Terrence (1997). The Symbolic Species: The Co-evolution of Language and the Brain. W.W. Norton. ISBN 0-571-17396-9.
  3. Jump up^ MacNeilage, Peter, 2008. The Origin of Speech. Oxford: Oxford University Press.
  4. Jump up^ Botha, R. and C. Knight (eds) 2009. The Cradle of Language. Oxford: Oxford University Press.
  5. Jump up^ Dor, D., C. Knight & J. Lewis (eds), 2014. The Social Origins of Language. Oxford: Oxford University Press.
  6. ^ Jump up to:a b Lewis, M. Paul, ed. (2009). Ethnologue: Languages of the World (16 ed.). Dallas: SIL International. ISBN 1-55671-216-2.
  7. Jump up^ “Simulated Evolution of Language: a Review of the Field”, Journal of Artificial Societies and Social Simulation vol. 5, no. 2
  8. Jump up^ Robert Spence, “A Functional Approach to Translation Studies. New systemic linguistic challenges in empirically informed didactics”, 2004, ISBN 3-89825-777-0, thesis. A pdf file

Unsolved Problems in Mathematics

Since the Renaissance, every century has seen the solution of more mathematical problems than the century before, and yet many mathematical problems, both major and minor, still elude solution.[1]

An unsolved problem in mathematics does not refer to the kind of problem found as an exercise in a textbook, but rather to the answer to a major question or a general method that provides a solution to an entire class of problems. Prizes are often awarded for the solution to a long-standing problem, and lists of unsolved problems receive considerable attention. This article reiterates the list of Millennium Prize Problems of unsolved problems in mathematics (includes problems ofphysics and computer science) as of August 2015, and lists further unsolved problems in algebra, additive and algebraic number theories, analysis, combinatorics,algebraic, discrete and Euclidean geometries, dynamical systems, partial differential equations, and graph, group, model, number, set and Ramsey theories, as well as miscellaneous unsolved problems. A list of problems solved since 1995 also appears, alongside some sources, general and specific, for the stated problems.

Lists of unsolved problems in mathematics

Over the course of time, several lists of unsolved mathematical problems have appeared. The following is a listing of those lists.

List Number of problems Proposed by Proposed in
Hilbert’s problems 23 David Hilbert 1900
Landau’s problems 4 Edmund Landau 1912
Taniyama’s problems[2] 36 Yutaka Taniyama 1955
Thurston’s 24 questions[3][4] 24 William Thurston 1982
Smale’s problems 18 Stephen Smale 1998
Millennium Prize problems 7 Clay Mathematics Institute 2000
Unsolved Problems in Mathematics for the 21st Century[5] 22 Jair Minoro Abe, Shotaro Tanaka 2001
DARPA’s math challenges[6][7] 23 DARPA 2007

Millennium Prize Problems

Of the original seven Millennium Prize Problems set by the Clay Mathematics Institute, six have yet to be solved, as of 2016:[8]

The seventh problem, the Poincaré conjecture, has been solved.[9] The smooth four-dimensional Poincaré conjecture—that is, whether a four-dimensional topological sphere can have two or more inequivalent smooth structures—is still unsolved.[10]

Unsolved problems

Additive number theory


Algebraic geometry

Algebraic number theory



Discrete geometry

Euclidean geometry

Dynamical systems

Graph theory

Group theory

Model theory

  • Vaught’s conjecture
  • The Cherlin–Zilber conjecture: A simple group whose first-order theory is stable in \aleph_0 is a simple algebraic group over an algebraically closed field.
  • The Main Gap conjecture, e.g. for uncountable first order theories, for AECs, and for \aleph_1-saturated models of a countable theory.[22]
  • Determine the structure of Keisler’s order[23][24]
  • The stable field conjecture: every infinite field with a stable first-order theory is separably closed.
  • Is the theory of the field of Laurent series over \mathbb{Z}_p decidable? of the field of polynomials over \mathbb{C}?
  • (BMTO) Is the Borel monadic theory of the real order decidable? (MTWO) Is the monadic theory of well-ordering consistently decidable?[25]
  • The Stable Forking Conjecture for simple theories[26]
  • For which number fields does Hilbert’s tenth problem hold?
  • Assume K is the class of models of a countable first order theory omitting countably many types. If K has a model of cardinality \aleph_{\omega_1} does it have a model of cardinality continuum?[27]
  • Shelah’s eventual Categority conjecture: For every cardinal \lambda there exists a cardinal \mu(\lambda) such that If an AEC K with LS(K)<= \lambda is categorical in a cardinal above \mu(\lambda) then it is categorical in all cardinals above \mu(\lambda).[22][28]
  • Shelah’s categoricity conjecture for L_{\omega_1,\omega}: If a sentence is categorical above the Hanf number then it is categorical in all cardinals above the Hanf number.[22]
  • Is there a logic L which satisfies both the Beth property and Δ-interpolation, is compact but does not satisfy the interpolation property?[29]
  • If the class of atomic models of a complete first order theory is categorical in the \aleph_n, is it categorical in every cardinal?[30][31]
  • Is every infinite, minimal field of characteristic zero algebraically closed? (minimal = no proper elementary substructure)
  • Kueker’s conjecture[32]
  • Does there exist an o-minimal first order theory with a trans-exponential (rapid growth) function?
  • Lachlan’s decision problem
  • Does a finitely presented homogeneous structure for a finite relational language have finitely many reducts?
  • Do the Henson graphs have the finite model property? (e.g. triangle-free graphs)
  • The universality problem for C-free graphs: For which finite sets C of graphs does the class of C-free countable graphs have a universal member under strong embeddings?[33]
  • The universality spectrum problem: Is there a first-order theory whose universality spectrum is minimum?[34]

Number theory (general)

Number theory (prime numbers)

Partial differential equations

Ramsey theory

Set theory


Problems solved since 1995


  1. Jump up^ Eves, An Introduction to the History of Mathematics 6th Edition, Thomson, 1990,ISBN 978-0-03-029558-4.
  2. Jump up^ Shimura, G. (1989). “Yutaka Taniyama and his time”. Bulletin of the London Mathematical Society 21 (2): 186–196. doi:10.1112/blms/21.2.186.
  3. Jump up^ http://www.uni-regensburg.de/Fakultaeten/nat_Fak_I/friedl/papers/dmv_091514.pdf
  5. Jump up^ Abe, Jair Minoro; Tanaka, Shotaro (2001). Unsolved Problems in Mathematics for the 21st Century. IOS Press. ISBN 9051994907.
  6. Jump up^ “DARPA invests in math”. CNN. 2008-10-14. Archived from the original on 2009-03-04. Retrieved 2013-01-14.
  7. Jump up^ “Broad Agency Announcement (BAA 07-68) for Defense Sciences Office (DSO)”. DARPA. 2007-09-10. Archived from the original on 2012-10-01. Retrieved 2013-06-25.
  8. Jump up^ “Millennium Problems”.
  9. Jump up^ “Poincaré Conjecture”. Clay Mathematics Institute. Archived from the originalon 2013-12-15.
  10. Jump up^ “Smooth 4-dimensional Poincare conjecture”.
  11. Jump up^ For background on the numbers that are the focus of this problem, see articles by Eric W. Weisstein, on pi ([1]), e ([2]), Khinchin’s Constant ([3]), irrational numbers ([4]), transcendental numbers ([5]), and irrationality measures ([6]) at Wolfram MathWorld, all articles accessed 15 December 2014.
  12. Jump up^ Michel Waldschmidt, 2008, “An introduction to irrationality and transcendence methods,” at The University of Arizona The Southwest Center for Arithmetic Geometry 2008 Arizona Winter School, March 15–19, 2008 (Special Functions and Transcendence), see [7], accessed 15 December 2014.
  13. Jump up^ John Albert, posting date unknown, “Some unsolved problems in number theory” [from Victor Klee & Stan Wagon, “Old and New Unsolved Problems in Plane Geometry and Number Theory”], in University of Oklahoma Math 4513 course materials, see [8], accessed 15 December 2014.
  14. Jump up^ Solution to the Counterfeit Coin Problem and its Generalization
  15. Jump up^ Socolar, Joshua E. S.; Taylor, Joan M. (2012), “Forcing nonperiodicity with a single tile”, The Mathematical Intelligencer 34 (1): 18–28, arXiv:1009.1419,doi:10.1007/s00283-011-9255-y, MR 2902144
  16. Jump up^ Matschke, Benjamin (2014), “A survey on the square peg problem”, Notices of the American Mathematical Society 61 (4): 346–253, doi:10.1090/noti1100
  17. Jump up^ Norwood, Rick; Poole, George; Laidacker, Michael (1992), “The worm problem of Leo Moser”, Discrete and Computational Geometry 7 (2): 153–162,doi:10.1007/BF02187832, MR 1139077
  18. Jump up^ Wagner, Neal R. (1976), “The Sofa Problem” (PDF), The American Mathematical Monthly 83 (3): 188–189, doi:10.2307/2977022,JSTOR 2977022
  19. Jump up^ Demaine, Erik D.; O’Rourke, Joseph (2007), “Chapter 22. Edge Unfolding of Polyhedra”, Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Cambridge University Press, pp. 306–338
  20. Jump up^ Bellos, Alex (11 August 2015), “Attack on the pentagon results in discovery of new mathematical tile”, The Guardian
  21. Jump up^ Kari, Jarkko (2009), “Structure of reversible cellular automata”, Unconventional Computation: 8th International Conference, UC 2009, Ponta Delgada, Portugal, September 7ÔÇô11, 2009, Proceedings, Lecture Notes in Computer Science 5715, Springer, p. 6, doi:10.1007/978-3-642-03745-0_5
  22. ^ Jump up to:a b c Shelah S, Classification Theory, North-Holland, 1990
  23. Jump up^ Keisler, HJ, “Ultraproducts which are not saturated.” J. Symb Logic 32 (1967) 23—46.
  24. Jump up^ Malliaris M, Shelah S, “A dividing line in simple unstable theories.”http://arxiv.org/abs/1208.2140
  25. Jump up^ Gurevich, Yuri, “Monadic Second-Order Theories,” in J. Barwise, S. Feferman, eds., Model-Theoretic Logics (New York: Springer-Verlag, 1985), 479–506.
  26. Jump up^ Peretz, Assaf, “Geometry of forking in simple theories.” J. Symbolic Logic Volume 71, Issue 1 (2006), 347–359.
  27. Jump up^ Shelah, Saharon (1999). “Borel sets with large squares”. Fundamenta Mathematicae 159 (1): 1–50. arXiv:math/9802134.
  28. Jump up^ Shelah, Saharon (2009). Classification theory for abstract elementary classes. College Publications. ISBN 978-1-904987-71-0.
  29. Jump up^ Makowsky J, “Compactness, embeddings and definability,” in Model-Theoretic Logics, eds Barwise and Feferman, Springer 1985 pps. 645–715.
  30. Jump up^ Baldwin, John T. (July 24, 2009). Categoricity (PDF). American Mathematical Society. ISBN 978-0821848937. Retrieved February 20, 2014.
  31. Jump up^ Shelah, Saharon. “Introduction to classification theory for abstract elementary classes”.
  32. Jump up^ Hrushovski, Ehud, “Kueker’s conjecture for stable theories.” Journal of Symbolic Logic Vol. 54, No. 1 (Mar., 1989), pp. 207–220.
  33. Jump up^ Cherlin, G.; Shelah, S. (May 2007). “Universal graphs with a forbidden subtree”.Journal of Combinatorial Theory, Series B 97 (3): 293–333. arXiv:math/0512218.doi:10.1016/j.jctb.2006.05.008.
  34. Jump up^ Džamonja, Mirna, “Club guessing and the universal models.” On PCF, ed. M. Foreman, (Banff, Alberta, 2004).
  35. Jump up^ “Are the Digits of Pi Random? Berkeley Lab Researcher May Hold Key”.
  36. Jump up^ Ribenboim, P. (2006). Die Welt der Primzahlen (in German) (2nd ed.). Springer. pp. 242–243. doi:10.1007/978-3-642-18079-8. ISBN 978-3-642-18078-1.
  37. Jump up^ Dobson, J. B. (June 2012) [2011], On Lerch’s formula for the Fermat quotient, p. 15, arXiv:1103.3907
  38. Jump up^ Barros, Manuel (1997), “General Helices and a Theorem of Lancret”, American Mathematical Society 125: 1503–1509, JSTOR 2162098
  39. Jump up^ http://arxiv.org/pdf/1605.00723v1.pdf
  40. Jump up^ Bourgain, Jean; Ciprian, Demeter; Larry, Guth (2015). “Proof of the main conjecture in Vinogradov’s Mean Value Theorem for degrees higher than three”.Annals of Mathematics.
  41. Jump up^ http://arxiv.org/pdf/1509.05363v5.pdf
  42. Jump up^ Proof of the umbral moonshine conjecture – Springer
  43. Jump up^ http://arxiv.org/pdf/1406.6534v10.pdf
  44. Jump up^ Helfgott, Harald A. (2013). “Major arcs for Goldbach’s theorem”.arXiv:1305.2897 [math.NT].
  45. Jump up^ Helfgott, Harald A. (2012). “Minor arcs for Goldbach’s problem”.arXiv:1205.5252 [math.NT].
  46. Jump up^ Helfgott, Harald A. (2013). “The ternary Goldbach conjecture is true”.arXiv:1312.7748 [math.NT].
  47. Jump up^ Casazza, Peter G.; Fickus, Matthew; Tremain, Janet C.; Weber, Eric (2006). Han, Deguang; Jorgensen, Palle E. T.; Larson, David Royal, eds. “The Kadison-Singer problem in mathematics and engineering: A detailed account”.Contemporary Mathematics. Large Deviations for Additive Functionals of Markov Chains: The 25th Great Plains Operator Theory Symposium, June 7–12, 2005, University of Central Florida, Florida (American Mathematical Society.) 414: 299–355. doi:10.1090/conm/414/07820. ISBN 978-0-8218-3923-2. Retrieved 24 April2015.
  48. Jump up^ Mackenzie, Dana. “Kadison–Singer Problem Solved” (PDF). SIAM News(January/February 2014) (Society for Industrial and Applied Mathematics). Retrieved 24 April 2015.
  49. Jump up^ http://arxiv.org/pdf/1204.2810v1.pdf
  50. Jump up^ http://www.math.jhu.edu/~js/Math646/brendle.lawson.pdf
  51. Jump up^ Marques, Fernando C.; Neves, André (2013). “Min-max theory and the Willmore conjecture”. Annals of Mathematics. arXiv:1202.6036.doi:10.4007/annals.2014.179.2.6.
  52. Jump up^ http://arxiv.org/pdf/1101.1330v4.pdf
  53. Jump up^ http://www.math.uiuc.edu/~mineyev/math/art/submult-shnc.pdf
  54. Jump up^ http://annals.math.princeton.edu/wp-content/uploads/annals-v174-n1-p11-p.pdf
  55. Jump up^ https://www.uni-due.de/~bm0032/publ/BlochKato.pdf
  56. Jump up^ page 359
  57. Jump up^ “motivic cohomology – Milnor-Bloch-Kato conjecture implies the Beilinson-Lichtenbaum conjecture – MathOverflow”.
  58. Jump up^ http://arxiv.org/pdf/1011.4105v3.pdf
  59. Jump up^ https://www.researchgate.net/profile/Juan_Souto3/publication/228365532_Non-realizability_and_ending_laminations_Proof_of_the_Density_Conjecture/links/541d85a10cf2218008d1d2e5.pdf
  60. Jump up^ Santos, Franciscos (2012). “A counterexample to the Hirsch conjecture”. Annals of Mathematics (Princeton University and Institute for Advanced Study) 176 (1): 383–412. doi:10.4007/annals.2012.176.1.7.
  61. Jump up^ Ziegler, Günter M. (2012). “Who solved the Hirsch conjecture?”. Documenta Mathematica. Extra Volume “Optimization Stories”: 75–85.
  62. Jump up^ “Generalized Sidon sets”.
  63. Jump up^ http://arxiv.org/pdf/0909.2360v3.pdf
  64. Jump up^ http://arxiv.org/pdf/0906.1612v2.pdf
  65. Jump up^ http://arxiv.org/pdf/0910.5501v5.pdf
  66. Jump up^ http://www.csie.ntu.edu.tw/~hil/bib/ChalopinG09.pdf
  67. Jump up^ http://arxiv.org/pdf/0809.4040.pdf
  68. ^ Jump up to:a b “Prize for Resolution of the Poincaré Conjecture Awarded to Dr. Grigoriy Perelman” (PDF) (Press release). Clay Mathematics Institute. March 18, 2010. Retrieved November 13, 2015. The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman.
  69. Jump up^ Khare, Chandrashekhar; Wintenberger, Jean-Pierre (2009), “Serre’s modularity conjecture (I)”, Inventiones Mathematicae 178 (3): 485–504, doi:10.1007/s00222-009-0205-7
  70. Jump up^ Khare, Chandrashekhar; Wintenberger, Jean-Pierre (2009), “Serre’s modularity conjecture (II)”, Inventiones Mathematicae 178 (3): 505–586, doi:10.1007/s00222-009-0206-6
  71. Jump up^ “2011 Cole Prize in Number Theory” (PDF). Notices of the AMS (Providence, Rhode Island, United States: American Mathematical Society) 58 (4): 610–611.ISSN 1088-9477. OCLC 34550461.
  72. Jump up^ http://www.ww.amc12.org/sites/default/files/pdf/pubs/SquaringThePlane.pdf
  73. Jump up^ http://arxiv.org/pdf/math/0509397.pdf
  74. Jump up^ Seigel-Itzkovich, Judy (2008-02-08). “Russian immigrant solves math puzzle”. The Jerusalem Post. Retrieved 2015-11-12.
  75. Jump up^ http://homepages.warwick.ac.uk/~masgak/papers/bhb-angel.pdf
  76. Jump up^ http://home.broadpark.no/~oddvark/angel/Angel.pdf
  77. Jump up^ http://homepages.warwick.ac.uk/~masibe/angel-mathe.pdf
  78. Jump up^ http://www.cs.bu.edu/~gacs/papers/angel.pdf
  79. Jump up^ http://www.ams.org/journals/proc/2005-133-09/S0002-9939-05-07752-X/S0002-9939-05-07752-X.pdf
  80. Jump up^ “Fields Medal – Ngô Bảo Châu”. International Congress of Mathematicians 2010. ICM. 19 August 2010. Retrieved 2015-11-12. Ngô Bảo Châu is being awarded the 2010 Fields Medal for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods.
  81. Jump up^ http://arxiv.org/pdf/math/0405568v1.pdf
  82. Jump up^ “Graph Theory”.
  83. Jump up^ Chung, Fan; Greene, Curtis; Hutchinson, Joan (April 2015). “Herbert S. Wilf (1931–2012)” (PDF). Notices of the AMS (Providence, Rhode Island, United States: American Mathematical Society) 62 (4): 358. ISSN 1088-9477.OCLC 34550461. The conjecture was finally given an exceptionally elegant proof by A. Marcus and G. Tardos in 2004.
  84. Jump up^ “Bombieri and Tao Receive King Faisal Prize” (PDF). Notices of the AMS(Providence, Rhode Island, United States: American Mathematical Society) 57 (5): 642–643. May 2010. ISSN 1088-9477. OCLC 34550461. Working with Ben Green, he proved there are arbitrarily long arithmetic progressions of prime numbers—a result now known as the Green–Tao theorem.
  85. Jump up^ http://arxiv.org/pdf/math/0412006v2.pdf
  86. Jump up^ Green, Ben (2004), “The Cameron–Erdős conjecture”, The Bulletin of the London Mathematical Society 36 (6): 769–778, arXiv:math.NT/0304058,doi:10.1112/S0024609304003650, MR 2083752
  87. Jump up^ “News from 2007”. American Mathematical Society. AMS. 31 December 2007. Retrieved 2015-11-13. The 2007 prize also recognizes Green for “his many outstanding results including his resolution of the Cameron-Erdős conjecture…”
  88. Jump up^http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_2003__98_/PMIHES_2003__98__1_0/PMIHES_2003__98__1_0.pdf
  89. Jump up^ “Kemnitz’ conjecture revisited”.
  90. Jump up^ http://www.ams.org/journals/jams/2004-17-01/S0894-0347-03-00440-5/S0894-0347-03-00440-5.pdf
  91. Jump up^ http://annals.math.princeton.edu/wp-content/uploads/annals-v158-n1-p04.pdf
  92. Jump up^ “The strong perfect graph theorem”.
  93. Jump up^ http://www.emis.de/journals/BAG/vol.43/no.1/b43h1haa.pdf
  94. Jump up^ Knight, R. W. (2002), The Vaught Conjecture: A Counterexample, manuscript
  95. Jump up^ http://www.ugr.es/~ritore/preprints/0406017.pdf
  96. Jump up^ Metsänkylä, Tauno (5 September 2003). “Catalan’s conjecture: another old diophantine problem solved” (PDF). Bulletin of the American Mathematical Society (American Mathematical Society) 41 (1): 43–57. ISSN 0273-0979. The conjecture, which dates back to 1844, was recently proven by the Swiss mathematician Preda Mihăilescu.
  97. Jump up^ http://www.ams.org/journals/jams/2001-14-04/S0894-0347-01-00373-3/S0894-0347-01-00373-3.pdf
  98. Jump up^ http://junon.u-3mrs.fr/monniaux/AHLMT02.pdf
  99. Jump up^ http://arxiv.org/pdf/math/0102150v4.pdf
  100. Jump up^ Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard (2001), “On the modularity of elliptic curves over Q: wild 3-adic exercises”, Journal of the American Mathematical Society 14 (4): 843–939, doi:10.1090/S0894-0347-01-00370-8, ISSN 0894-0347, MR 1839918
  101. Jump up^ http://www.ams.org/journals/mcom/2001-70-234/S0025-5718-00-01178-9/S0025-5718-00-01178-9.pdf
  102. Jump up^ http://intlpress.com/site/pub/files/_fulltext/journals/sdg/2002/0007/0001/SDG-2002-0007-0001-a001.pdf
  103. Jump up^ Croot, Ernest S., III (2000), Unit Fractions, Ph.D. thesis, University of Georgia, Athens. Croot, Ernest S., III (2003), “On a coloring conjecture about unit fractions”,Annals of Mathematics 157 (2): 545–556, arXiv:math.NT/0311421,doi:10.4007/annals.2003.157.545
  104. Jump up^ http://arxiv.org/pdf/math/9906042v2.pdf
  105. Jump up^ http://arxiv.org/pdf/math/9906212v2.pdf
  106. Jump up^ Ullmo, E. (1998), “Positivité et Discrétion des Points Algébriques des Courbes”, Annals of Mathematics 147 (1): 167–179, doi:10.2307/120987, Zbl 0934.14013
  107. Jump up^ Zhang, S.-W. (1998), “Equidistribution of small points on abelian varieties”, Annals of Mathematics 147 (1): 159–165, doi:10.2307/120986
  108. Jump up^ Lafforgue, Laurent (1998), “Chtoucas de Drinfeld et applications” [Drinfelʹd shtukas and applications], Documenta Mathematica (in French) II: 563–570,ISSN 1431-0635, MR 1648105
  109. Jump up^ http://arxiv.org/pdf/1501.02155.pdf
  110. Jump up^ http://arxiv.org/pdf/math/9811079v3.pdf
  111. Jump up^ Norio Iwase (1 November 1998). “Ganea’s Conjecture on Lusternik-Schnirelmann Category”. ResearchGate.
  112. Jump up^ Merel, Loïc (1996). “Bornes pour la torsion des courbes elliptiques sur les corps de nombres” [Bounds for the torsion of elliptic curves over number fields]. Inventiones Mathematicae (in French) 124 (1): 437–449. doi:10.1007/s002220050059. MR 1369424
  113. Jump up^https://www.researchgate.net/profile/Zhibo_Chen/publication/220188021_Harary’s_conjectures_on_integral_sum_graphs/links/5422b2490cf290c9e3aac7fe.pdf
  114. Jump up^ Wiles, Andrew (1995). “Modular elliptic curves and Fermat’s Last Theorem”(PDF). Annals of Mathematics (Annals of Mathematics) 141 (3): 443–551.doi:10.2307/2118559. JSTOR 2118559. OCLC 37032255.
  115. Jump up^ Taylor R, Wiles A (1995). “Ring theoretic properties of certain Hecke algebras”.Annals of Mathematics (Annals of Mathematics) 141 (3): 553–572.doi:10.2307/2118560. JSTOR 2118560. OCLC 37032255.

Further reading

Books discussing recently solved problems[dated info]

Books discussing unsolved problems

  • Fan Chung; Graham, Ron (1999). Erdos on Graphs: His Legacy of Unsolved Problems. AK Peters. ISBN 1-56881-111-X.
  • Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1994). Unsolved Problems in Geometry. Springer. ISBN 0-387-97506-3.
  • Guy, Richard K. (2004). Unsolved Problems in Number Theory. Springer. ISBN 0-387-20860-7.
  • Klee, Victor; Wagon, Stan (1996). Old and New Unsolved Problems in Plane Geometry and Number Theory. The Mathematical Association of America. ISBN 0-88385-315-9.
  • Du Sautoy, Marcus (2003). The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics. Harper Collins. ISBN 0-06-093558-8.
  • Derbyshire, John (2003). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Joseph Henry Press. ISBN 0-309-08549-7.
  • Devlin, Keith (2006). The Millennium Problems – The Seven Greatest Unsolved* Mathematical Puzzles Of Our Time. Barnes & Noble. ISBN 978-0-7607-8659-8.
  • Blondel, Vincent D.; Megrestski, Alexandre (2004). Unsolved problems in mathematical systems and control theory. Princeton University Press. ISBN 0-691-11748-9.
  • Lizhen Ji, [various]; Yat-Sun Poon, Shing-Tung Yau (2013). Open Problems and Surveys of Contemporary Mathematics (volume 6 in the Surveys in Modern Mathematics series) (Surveys of Modern Mathematics). International Press of Boston. ISBN 1-571-46278-3.
  • Waldschmidt, Michel (2004). “Open Diophantine Problems” (PDF). Moscow Mathematical Journal 4 (1): 245–305. ISSN 1609-3321. Zbl 1066.11030.
  • Mazurov, V. D.; Khukhro, E. I. (1 Jun 2015). “Unsolved Problems in Group Theory. The Kourovka Notebook. No. 18 (English version)”. arXiv:1401.0300v6.
  • Derbyshire, John (2003). Prime Obsession. The Joseph Henry Press. ISBN 0-309-08549-7.

External links

Unsolved Problems in Medicine

This article lists currently unsolved problems in medicine.

Problems or unknown causes for diseases

(Note: Current diseases being researched for cures are not on this list e.g. Cancer, due to usually using available knowledge of the causes and epidemiology to manage symptoms, having treatments already available for that ailment or find a cure through their based epidemiological vectors.)

Unsolved Problems in Neuroscience

There are yet unsolved problems in neuroscience, although some of these problems have evidence supporting a hypothesized solution, and the field is rapidly evolving. These problems include:


  1. Jump up^ Sejnowski, Terrence J.; Hemmen, J. L. van (2006). 23 problems in systems neuroscience (PDF). Oxford [Oxfordshire]: Oxford University Press. ISBN 0-19-514822-3.
  2. Jump up^ Tononi, G; Koch, C. (2015). “Consciousness: Here, there and everywhere?” (PDF). Philosophical Transactions of the Royal Society London B.
  3. Jump up^ University of Copenhagen (24 January 2007). “Thinking With The Spinal Cord?”. ScienceDaily. Retrieved 25 May 2016.
  4. Jump up^ A Database Of All Things Brainy

External links

Unsolved Problems in Philosophy

This is a list of some of the major unsolved problems in philosophy. Clearly, unsolved philosophical problems exist in the lay sense (e.g. “What is the meaning of life?“, “Where did we come from?“, “What is reality?“, etc.). However, professional philosophers generally accord serious philosophical problems specific names or questions, which indicate a particular method of attack or line of reasoning. As a result, broad and untenable topics become manageable. It would therefore be beyond the scope of this article to categorize “life” (and similar vague categories) as an unsolved philosophical problem.



Main article: Essentialism

In art, essentialism is the idea that each medium has its own particular strengths and weaknesses, contingent on its mode of communication. A chase scene, for example, may be appropriate for motion pictures, but poorly realized in poetry, because the essential components of the poetic medium are ill suited to convey the information of a chase scene. This idea may be further refined, and it may be said that the haiku is a poor vehicle for describing a lover’s affection, as opposed to the sonnet. Essentialism is attractive to artists, because it not only delineates the role of art and media, but also prescribes a method for evaluating art (quality correlates to the degree of organic form). However, considerable criticism has been leveled at essentialism, which has been unable to formally define organic form or for that matter, medium. What, after all, is the medium of poetry? If it is language, how is this distinct from the medium of prose fiction? Is the distinction really a distinction in medium or genre? Questions about organic form, its definition, and its role in art remain controversial. Generally, working artists accept some form of the concept of organic form, whereas philosophers have tended to regard it as vague and irrelevant.

Art objects

This problem originally arose from the practice rather than theory of art. Marcel Duchamp, in the 20th century, challenged conventional notions of what “art” is, placing ordinary objects in galleries to prove that the context rather than content of an art piece determines what art is. In music, John Cage followed up on Duchamp’s ideas, asserting that the term “music” applied simply to the sounds heard within a fixed interval of time.

While it is easy to dismiss these assertions, further investigation[who?] shows that Duchamp and Cage are not so easily disproved. For example, if a pianist plays aChopin etude, but his finger slips missing one note, is it still the Chopin etude or a new piece of music entirely? Most people would agree that it is still a Chopin etude (albeit with a missing note), which brings into play the Sorites paradox, mentioned below. If one accepts that this is not a fundamentally changed work of music, however, is one implicitly agreeing with Cage that it is merely the duration and context of musical performance, rather than the precise content, which determines what music is? Hence, the question is what the criteria for art objects are and whether these criteria are entirely context-dependent.


Epistemological problems are concerned with the nature, scope and limitations of knowledge. Epistemology may also be described as the study of knowledge.

Gettier problem

Main article: Gettier problem

Plato suggests, in his Theaetetus (210a) and Meno (97a–98b), that “knowledge” may be defined as justified true belief. For over two millennia, this definition of knowledge has been reinforced and accepted by subsequent philosophers. An item of information’s justifiability, truth, and belief have been seen as the necessary and sufficient conditions for knowledge.

In 1963, however, Edmund Gettier published an article in the periodical Analysis entitled “Is Justified True Belief Knowledge?”, offering instances of justified true belief that do not conform to the generally understood meaning of “knowledge.” Gettier’s examples hinged on instances of epistemic luck: cases where a person appears to have sound evidence for a proposition, and that proposition is in fact true, but the apparent evidence is not causally related to the proposition’s truth.

In response to Gettier’s article, numerous philosophers[who?] have offered modified criteria for “knowledge.” There is no general consensus to adopt any of the modified definitions yet proposed.

Problem of the criterion

Overlooking for a moment the complications posed by Gettier problems, philosophy has essentially continued to operate on the principle that knowledge is justified true belief. The obvious question that this definition entails is how one can know whether one’s justification is sound. One must therefore provide a justification for the justification. That justification itself requires justification, and the questioning continues interminably.

The conclusion is that no one can truly have knowledge of anything, since it is, due to this infinite regression, impossible to satisfy the justification element. In practice, this has caused little concern to philosophers, since the demarcation between a reasonably exhaustive investigation and superfluous investigation is usually clear.

Others argue for forms of coherentist systems, e.g. Susan Haack. Recent work by Peter D. Klein[1] views knowledge as essentially defeasible. Therefore, an infinite regress is unproblematic, since any known fact may be overthrown on sufficiently in depth investigation.

Molyneux problem

Main article: Molyneux’s problem

The Molyneux problem dates back to the following question posed by William Molyneux to John Locke in the 17th century: if a man born blind, and able to distinguish by touch between a cube and a globe, were made to see, could he now tell by sight which was the cube and which the globe, before he touched them? The problem raises fundamental issues in epistemology and the philosophy of mind, and was widely discussed after Locke included it in the second edition of hisEssay Concerning Human Understanding.[2]

A similar problem was also addressed earlier in the 12th century by Ibn Tufail (Abubacer), in his philosophical novel, Hayy ibn Yaqdhan (Philosophus Autodidactus). His version of the problem, however, dealt mainly with colors rather than shapes.[3][4]

Modern science may now have the tools necessary to test this problem in controlled environments. The resolution of this problem is in some sense provided by the study of human subjects who gain vision after extended congenital blindness. One such subject took approximately a year to recognize most household objects purely by sight.[citation needed] This indicates that this may no longer be an unsolved problem in philosophy.

Münchhausen trilemma

The Münchhausen trilemma, also called Agrippa‘s trilemma, purports that it is impossible to prove any certain truth even in fields such as logic and mathematics. According to this argument, the proof of any theory rests either on circular reasoning, infinite regress, or unproven axioms.


See also: Distinguishing blue from green in language

The question hinges on whether color is a product of the mind or an inherent property of objects. While most philosophers will agree that color assignment corresponds to spectra of light frequencies, it is not at all clear whether the particular psychological phenomena of color are imposed on these visual signals by the mind, or whether such qualia are somehow naturally associated with their noumena. Another way to look at this question is to assume two people (“Fred” and “George” for the sake of convenience) see colors differently. That is, when Fred sees the sky, his mind interprets this light signal as blue. He calls the sky “blue.” However, when George sees the sky, his mind assigns green to that light frequency. If Fred were able to step into George’s mind, he would be amazed that George saw green skies. However, George has learned to associate the word “blue” with what his mind sees as green, and so he calls the sky “blue”, because for him the color green has the name “blue.” The question is whether blue must be blue for all people, or whether the perception of that particular color is assigned by the mind.

This extends to all areas of the physical reality, where the outside world we perceive is merely a representation of what is impressed upon the senses. The objects we see are in truth wave-emitting (or reflecting) objects which the brain shows to the conscious self in various forms and colors. Whether the colors and forms experienced perfectly match between person to person, may never be known. That people can communicate accurately shows that the order and proportionality in which experience is interpreted is generally reliable. Thus one’s reality is, at least, compatible to another person’s in terms of structure and ratio.


Moral luck

Main article: Moral luck

The problem of moral luck is that some people are born into, live within, and experience circumstances that seem to change their moral culpability when all other factors remain the same.

For instance, a case of circumstantial moral luck: a poor person is born into a poor family, and has no other way to feed himself so he steals his food. Another person, born into a very wealthy family, does very little but has ample food and does not need to steal to get it. Should the poor person be more morally blameworthy than the rich person? After all, it is not his fault that he was born into such circumstances, but a matter of “luck”.

A related case is resultant moral luck. For instance, two persons behave in a morally culpable way, such as driving carelessly, but end up producing unequal amounts of harm: one strikes a pedestrian and kills him, while the other does not. That one driver caused a death and the other did not is no part of the drivers’ intentional actions; yet most observers would likely ascribe greater blame to the driver who killed (compare consequentialism and choice).

The fundamental question of moral luck is how our moral responsibility is changed by factors over which we have no control.

Moral knowledge

Are moral facts possible, what do they consist in, and how do we come to know them? Rightness and wrongness seem strange kinds of entities, and different from the usual properties of things in the world, such as wetness, being red, or solidity. Richmond Campbell[5] has outlined these kinds of issues in his encyclopedia article Moral Epistemology.

In particular, he considers three alternative explanations of moral facts as: theological, (supernatural, the commands of God); non-natural (based on intuitions); or simply natural properties (such as leading to pleasure or to happiness). There are cogent arguments against each of these alternative accounts, he claims, and there has not been any fourth alternative proposed. So the existence of moral knowledge and moral facts remains dubious and in need of further investigation. But moral knowledge supposedly already plays an important part in our everyday thinking, in our legal systems and criminal investigations.

Philosophy of mathematics

Mathematical objects

What are numbers, sets, groups, points, etc.? Are they real objects or are they simply relationships that necessarily exist in all structures? Although many disparate views exist regarding what a mathematical object is, the discussion may be roughly partitioned into two opposing schools of thought: platonism, which asserts that mathematical objects are real, and formalism, which asserts that mathematical objects are merely formal constructions. This dispute may be better understood when considering specific examples, such as the “continuum hypothesis“. The continuum hypothesis has been proven independent of the ZF axioms of set theory, so according to that system, the proposition can neither be proven true nor proven false. A formalist would therefore say that the continuum hypothesis is neither true nor false, unless you further refine the context of the question. A platonist, however, would assert that there either does or does not exist a transfinite set with acardinality less than the continuum but greater than any countable set.[citation needed] So, regardless of whether it has been proven unprovable, the platonist would argue that an answer nonetheless does exist.


Sorites paradox

Main article: Sorites paradox

Otherwise known as the “paradox of the heap”, the question regards how one defines a “thing.” Is a bale of hay still a bale of hay if you remove one straw? If so, is it still a bale of hay if you remove another straw? If you continue this way, you will eventually deplete the entire bale of hay, and the question is: at what point is it no longer a bale of hay? While this may initially seem like a superficial problem, it penetrates to fundamental issues regarding how we define objects. This is similar toTheseus’ paradox and the Continuum fallacy.


A counterfactual is a statement that follows this form: “If Joseph Swan had not invented the modern incandescent light bulb, then someone else would have invented it anyway.” People use counterfactuals every day; however, its analysis is not so clear. Swan, after all, did invent the modern incandescent light bulb, so how can the statement be true, if it is impossible to examine its correspondence to reality? (See correspondence theory of truth.) Similar statements have the form, “If you don’t eat your meat, then you can’t have any pudding.” This is another clear if-then statement, which is not verifiable (assuming the addressee did eat his/her meat). Two proposed analyses have resulted from this question. First, some philosophers assert that background information is assumed when stating and interpreting counterfactual conditionals. In the case of the Swan statement, certain trends in the history of technology, the utility of artificial light, and the discovery of electricity may all provide evidence for a logically sound argument. However, other philosophers assert that a modal “possible world” theory offers a more accurate description of counterfactual conditionals. According to this analysis, in the Swan example one would consider the closest possible world to the real world in whichSwan did not create the modern incandescent light bulb. When a counterfactual is used as an argument to justify an illegal act, it is known as the dirty hands argument. For example, “if I didn’t sell him drugs then someone else would have, and those drugs might not have been cut or more harmful.”

Material implication

Main article: Material conditional

People have a pretty clear idea what if-then means. In formal logic however, material implication defines if-then, which is not consistent with the common understanding of conditionals. In formal logic, the statement “If today is Saturday, then 1+1=2” is true. However, ‘1+1=2’ is true regardless of the content of the antecedent; a causal or meaningful relation is not required. The statement as a whole must be true, because 1+1=2 cannot be false. (If it could, then on a given Saturday, so could the statement). Formal logic has shown itself extremely useful in formalizing argumentation, philosophical reasoning, and mathematics. The discrepancy between material implication and the general conception of conditionals however is a topic of intense investigation: whether it is an inadequacy in formal logic, an ambiguity of ordinary language, or as championed by H.P. Grice, that no discrepancy exists.

Philosophy of mind

Mind–body problem

The mind–body problem is the problem of determining the relationship between the human body and the human mind. Philosophical positions on this question are generally predicated on either a reduction of one to the other, or a belief in the discrete coexistence of both. This problem is usually exemplified by Descartes, who championed a dualistic picture. The problem therein is to establish how the mind and body communicate in a dualistic framework. Neurobiology and emergencehave further complicated the problem by allowing the material functions of the mind to be a representation of some further aspect emerging from the mechanistic properties of the brain. The brain essentially stops generating conscious thought during deep sleep; the ability to restore such a pattern remains a mystery to science and is a subject of current research (see also neurophilosophy).

Cognition and AI

This problem actually defines a field, however its pursuits are specific and easily stated. Firstly, what are the criteria for intelligence? What are the necessary components for defining consciousness? Secondly, how can an outside observer test for these criteria? The “Turing Test” is often cited as a prototypical test of consciousness, although it is almost universally regarded as insufficient. It involves a conversation between a sentient being and a machine, and if the being can’t tell he is talking to a machine, it is considered intelligent. A well trained machine, however, could theoretically “parrot” its way through the test. This raises the corollary question of whether it is possible to artificially create consciousness (usually in the context of computers or machines), and of how to tell a well trained mimic from a sentient entity.

Important thought in this area includes most notably: John Searle‘s Chinese Room, Hubert Dreyfus‘ non-cognitivist critique, as well as Hilary Putnam‘s work onFunctionalism.

A related field is the ethics of artificial intelligence, which addresses such problems as the existence of moral personhood of AIs, the possibility of moral obligationsto AIs (for instance, the right of a possibly sentient computer system to not be turned off), and the question of making AIs that behave ethically towards humans and others.

Hard problem of consciousness

The hard problem of consciousness is the question of what consciousness is and why we have consciousness as opposed to being philosophical zombies. The adjective “hard” is to contrast with the “easy” consciousness problems, which seek to explain the mechanisms of consciousness (“why” versus “how,” or final causeversus efficient cause). The hard problem of consciousness is questioning whether all beings undergo an experience of consciousness rather than questioning the neurological makeup of beings.

Philosophy of science

Problem of induction

Main article: Problem of induction

Intuitively, it seems to be the case that we know certain things with absolute, complete, utter, unshakable certainty. For example, if you travel to the Arctic and touch an iceberg, you know that it would feel cold. These things that we know from experience are known through induction. The problem of induction in short; (1) any inductive statement (like the sun will rise tomorrow) can only be deductively shown if one assumes that nature is uniform. (2) the only way to show that nature is uniform is by using induction. Thus induction cannot be justified deductively.

Demarcation problem

Main article: Demarcation problem

‘The problem of demarcation’ is an expression introduced by Karl Popper to refer to ‘the problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as “metaphysical” systems on the other’. Popper attributes this problem to Kant. Although Popper mentions mathematics and logic, other writers focus on distinguishing science from metaphysics and pseudo-science.

Some, including Popper, raise the problem because of an intellectual desire to clarify this distinction.[citation needed] Logical positivists had, in addition, a social and intellectual agenda to discredit non-scientific disciplines.[citation needed]


Main article: Scientific realism

Does a world independent of human beliefs and representations exist? Is such a world empirically accessible, or would such a world be forever beyond the bounds of human sense and hence unknowable? Can human activity and agency change the objective structure of the world? These questions continue to receive much attention in the philosophy of science. A clear “yes” to the first question is a hallmark of the scientific realism perspective. Philosophers such as Bas van Fraassenhave important and interesting answers to the second question. In addition to the realism vs. empiricism axis of debate, there is a realism vs. social constructivismaxis which heats many academic passions. With respect to the third question, Paul Boghossian‘s “Fear of Knowledge: Against Relativism and Constructivism”. Oxford University Press. 2006. is a powerful critique of social constructivism, for instance. Ian Hacking’s The Social Construction of What? (Harvard UP, 2000) constitutes a more moderate critique of constructivism, which usefully disambiguates confusing polysemy of the term “constructivism.”

See also


  1. Jump up^ Klein, P. D., “Human Knowledge and the Infinite Progress of Reasoning,” Philosophical Studies, 134. 1, 2007, 1-17.
  2. Jump up^ Locke, John. An Essay Concerning Human Understanding, Book 2, Chapter 9.

    “I shall here insert a problem of that very ingenious and studious promoter of real knowledge, the learned and worthy Mr. Molyneux, which he was pleased to send me in a letter some months since; and it is this:—”Suppose a man born blind, and now adult, and taught by his touch to distinguish between a cube and a sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt one and the other, which is the cube, which the sphere. Suppose then the cube and sphere placed on a table, and the blind man be made to see: quaere, whether by his sight, before he touched them, he could now distinguish and tell which is the globe, which the cube?” To which the acute and judicious proposer answers, “Not. For, though he has obtained the experience of how a globe, how a cube affects his touch, yet he has not yet obtained the experience, that what affects his touch so or so, must affect his sight so or so; or that a protuberant angle in the cube, that pressed his hand unequally, shall appear to his eye as it does in the cube.”—I agree with this thinking gentleman, whom I am proud to call my friend, in his answer to this problem; and am of opinion that the blind man, at first sight, would not be able with certainty to say which was the globe, which the cube, whilst he only saw them; though he could unerringly name them by his touch, and certainly distinguish them by the difference of their figures felt. This I have set down, and leave with my reader, as an occasion for him to consider how much he may be beholden to experience, improvement, and acquired notions, where he thinks he had not the least use of, or help from them. And the rather, because this observing gentleman further adds, that “having, upon the occasion of my book, proposed this to divers very ingenious men, he hardly ever met with one that at first gave the answer to it which he thinks true, till by hearing his reasons they were convinced.”

  3. Jump up^ Muhammad ibn Abd al-Malik Ibn Tufayl and Léon Gauthier (1981), Risalat Hayy ibn Yaqzan, p. 5, Editions de la Méditerranée.

    “If you want a comparison that will make you clearly grasp the difference between the perception, such as it is understood by that sect [the Sufis] and the perception as others understand it, imagine a person born blind, endowed however with a happy natural temperament, with a lively and firm intelligence, a surememory, a straight sprite, who grew up from the time he was an infant in a city where he never stopped learning, by means of the senses he did dispose of, to know the inhabitants individually, the numerous species of beings, living as well as non-living, there, the streets and sidestreets, the houses, the steps, in such a manner as to be able to cross the city without a guide, and to recognize immediately those he met; the colors alone would not be known to him except by the names they bore, and by certain definitions that designated them. Suppose that he had arrived at this point and suddenly, his eyes were opened, he recovered his view, and he crosses the entire city, making a tour of it. He would find no object different from the idea he had made of it; he would encounter nothing he didn’t recognize, he would find the colors conformable to the descriptions of them that had been given to him; and in this there would only be two new important things for him, one the consequence of the other: a clarity, a greater brightness, and a great voluptuousness.”

  4. Jump up^ Lobel, Diana. A Sufi-Jewish Dialogue: Philosophy and Mysticism in Baḥya Ibn Paqūda’s Duties of the Heart, University of Pennsylvania Press, 2006, p.24. ISBN 0-8122-3953-9
  5. Jump up^ Campbell, Richmond, “Moral Epistemology”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.)

Unsolved Problems in Physics

Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.

Unsolved problems by subfield

The following is a list of unsolved problems grouped into broad area of physics.[1]

General physics/quantum physics

Entropy (arrow of time)
Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics?[2] Why areCP violations observed in certain weak force decays, but not elsewhere? Are CP violations somehow a product of the Second Law of Thermodynamics, or are they a separate arrow of time? Are there exceptions to the principle of causality? Is there a single possible past? Is the present moment physically distinct from the past and future or is it merely an emergent property of consciousness? Why does time have a direction? What links the quantum arrow of time to the thermodynamic arrow?
Interpretation of quantum mechanics
How does the quantum description of reality, which includes elements such as the superposition of states and wavefunction collapse or quantum decoherence, give rise to the reality we perceive? Another way of stating this question regards the measurement problem: What constitutes a “measurement” which causes the wave function to collapse into a definite state? Unlike classical physical processes, some quantum mechanical processes (such as quantum teleportationarising from quantum entanglement) cannot be simultaneously “local”, “causal”, and “real”, but it is not obvious which of these properties must be sacrificed or if an attempt to describe quantum mechanical processes in these senses is a category error such that a proper understanding of quantum mechanics would render the question meaningless.
Grand Unification Theory (“Theory of everything“)
Is there a theory which explains the values of all fundamental physical constants?[2] Is the theory string theory? Is there a theory which explains why the gauge groups of the standard model are as they are, why observed spacetime has 3 spatial dimensions and 1 temporal dimension, and why all laws of physics are as they are? Do “fundamental physical constants” vary over time? Are any of the particles in the standard model of particle physics actually composite particles too tightly bound to observe as such at current experimental energies? Are there fundamental particles that have not yet been observed, and, if so, which ones are they and what are their properties? Are there unobserved fundamental forces implied by a theory that explains other unsolved problems in physics?
Yang–Mills theory
Given an arbitrary compact gauge group, does a non-trivial quantum Yang–Mills theory with a finite mass gap exist? This problem is also listed as one of theMillennium Prize Problems in mathematics.
Physical information
Are there physical phenomena, such as wave function collapse or black holes, which irrevocably destroy information about their prior states? How is quantum information stored as a state of a quantum system?
Dimensionless physical constant
At the present time, the values of the dimensionless physical constants cannot be calculated; they are determined only by physical measurement.[3][4] What is the minimum number of dimensionless physical constants from which all other dimensionless physical constants can be derived? Are dimensionful physical constants necessary at all?
Fine-tuned Universe
What explains why the fundamental physical constants are set in the narrow range that is necessary to support carbon-based life?

Cosmology and general relativity

Problem of time
How can time be reconciled with general relativity?
Cosmic inflation
Is the theory of cosmic inflation correct, and, if so, what are the details of this epoch? What is the hypothetical inflaton field giving rise to inflation? If inflation happened at one point, is it self-sustaining through inflation of quantum-mechanical fluctuations, and thus ongoing in some extremely distant place?[5]
Horizon problem
Why is the distant universe so homogeneous when the Big Bang theory seems to predict larger measurable anisotropies of the night sky than those observed? Cosmological inflation is generally accepted as the solution, but are other possible explanations such as a variable speed of light more appropriate?[6]
Future of the universe
Is the universe heading towards a Big Freeze, a Big Rip, a Big Crunch, or a Big Bounce? Or is it part of an infinitely recurring cyclic model?
Baryon asymmetry
Why is there far more matter than antimatter in the observable universe?
Cosmological constant problem
Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?[7]

Estimated distribution of dark matter and dark energy in the universe.

Dark matter
What is the identity of dark matter?[6] Is it a particle? Is it the lightest superpartner (LSP)? Do the phenomena attributed to dark matter point not to some form of matter but actually to an extension of gravity?
Dark energy
What is the cause of the observed accelerated expansion (de Sitter phase) of the Universe? Why is the energy density of the dark energy component of the same magnitude as the density of matter at present when the two evolve quite differently over time; could it be simply that we are observing at exactly the right time? Is dark energy a pure cosmological constant or are models of quintessence such as phantom energy applicable?
Dark flow
Is a non-spherically symmetric gravitational pull from outside the observable Universe responsible for some of the observed motion of large objects such as galactic clusters in the universe?
Ecliptic alignment of CMB anisotropy
Some large features of the microwave sky at distances of over 13 billion light years appear to be aligned with both the motion and orientation of the solar system. Is this due to systematic errors in processing, contamination of results by local effects, or an unexplained violation of the Copernican principle?
Shape of the Universe
What is the 3-manifold of comoving space, i.e. of a comoving spatial section of the Universe, informally called the “shape” of the Universe? Neither the curvature nor the topology is presently known, though the curvature is known to be “close” to zero on observable scales. The cosmic inflation hypothesis suggests that the shape of the Universe may be unmeasurable, but, since 2003, Jean-Pierre Luminet, et al., and other groups have suggested that the shape of the Universe may be the Poincaré dodecahedral space. Is the shape unmeasurable; the Poincaré space; or another 3-manifold?

Quantum gravity

Vacuum catastrophe
Why does the predicted mass of the quantum vacuum have little effect on the expansion of the universe?
Quantum gravity
Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)?[8] Is spacetime fundamentally continuous or discrete? Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)? Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?
Black holes, black hole information paradox, and black hole radiation
Do black holes produce thermal radiation, as expected on theoretical grounds? Does this radiation contain information about their inner structure, as suggested by gauge–gravity duality, or not, as implied by Hawking‘s original calculation? If not, and black holes can evaporate away, what happens to the information stored in them (since quantum mechanics does not provide for the destruction of information)? Or does the radiation stop at some point leaving black hole remnants? Is there another way to probe their internal structure somehow, if such a structure even exists?
Extra dimensions
Does nature have more than four spacetime dimensions? If so, what is their size? Are dimensions a fundamental property of the universe or an emergent result of other physical laws? Can we experimentally observe evidence of higher spatial dimensions?
The cosmic censorship hypothesis and the chronology protection conjecture
Can singularities not hidden behind an event horizon, known as “naked singularities“, arise from realistic initial conditions, or is it possible to prove some version of the “cosmic censorship hypothesis” of Roger Penrose which proposes that this is impossible?[9] Similarly, will the closed timelike curves which arise in some solutions to the equations of general relativity (and which imply the possibility of backwards time travel) be ruled out by a theory of quantum gravity which unites general relativity with quantum mechanics, as suggested by the “chronology protection conjecture” of Stephen Hawking?
Are there non-local phenomena in quantum physics? If they exist, are non-local phenomena limited to the entanglement revealed in the violations of the Bell inequalities, or can information and conserved quantities also move in a non-local way? Under what circumstances are non-local phenomena observed? What does the existence or absence of non-local phenomena imply about the fundamental structure of spacetime? How does this relate to quantum entanglement? How does this elucidate the proper interpretation of the fundamental nature of quantum physics?

High-energy physics/particle physics

Higgs mechanism
Are the branching ratios of the Higgs boson decays consistent with the standard model? Is there only one type of Higgs boson?
Hierarchy problem
Why is gravity such a weak force? It becomes strong for particles only at the Planck scale, around 1019 GeV, much above the electroweak scale (100 GeV, the energy scale dominating physics at low energies). Why are these scales so different from each other? What prevents quantities at the electroweak scale, such as the Higgs boson mass, from getting quantum corrections on the order of the Planck scale? Is the solution supersymmetry, extra dimensions, or just anthropicfine-tuning?
Magnetic monopoles
Did particles that carry “magnetic charge” exist in some past, higher-energy epoch? If so, do any remain today? (Paul Dirac showed the existence of some types of magnetic monopoles would explain charge quantization.)[10]
Proton decay and spin crisis
Is the proton fundamentally stable? Or does it decay with a finite lifetime as predicted by some extensions to the standard model?[11] How do the quarks and gluons carry the spin of protons?[12]
Is spacetime supersymmetry realized at TeV scale? If so, what is the mechanism of supersymmetry breaking? Does supersymmetry stabilize the electroweak scale, preventing high quantum corrections? Does the lightest supersymmetric particle (LSP or Lightest Supersymmetric Particle) comprise dark matter?
Generations of matter
Why are there three generations of quarks and leptons? Is there a theory that can explain the masses of particular quarks and leptons in particular generations from first principles (a theory of Yukawa couplings)?[13]
Neutrino mass
What is the mass of neutrinos, whether they follow Dirac or Majorana statistics? Is mass hierarchy normal or inverted? Is the CP violating phase 0?[14][15][16]
Color confinement
Why has there never been measured a free quark or gluon, but only objects that are built out of them, such as mesons and baryons? How does this phenomenon emerge from QCD?
Strong CP problem and axions
Why is the strong nuclear interaction invariant to parity and charge conjugation? Is Peccei–Quinn theory the solution to this problem?
Anomalous magnetic dipole moment
Why is the experimentally measured value of the muon‘s anomalous magnetic dipole moment (“muon g−2”) significantly different from the theoretically predicted value of that physical constant?[17]
Proton size puzzle
What is the electric charge radius of the proton? How does it differ from gluonic charge?
Pentaquarks and other exotic hadrons
What combinations of quarks are possible? Why were pentaquarks so difficult to discover?[18] Are they a tightly-bound system of five elementary particles, or a more weakly-bound pairing of a baryon and a meson?[19]

Astronomy and astrophysics

Relativistic jet. The environment around theAGN where the relativistic plasma is collimated into jets which escape along the pole of thesupermassive black hole.

Astrophysical jet
Why do the accretion discs surrounding certain astronomical objects, such as the nuclei of active galaxies, emitrelativistic jets along their polar axes?[20] Why are there quasi-periodic oscillations in many accretion discs?[21]Why does the period of these oscillations scale as the inverse of the mass of the central object?[22] Why are there sometimes overtones, and why do these appear at different frequency ratios in different objects?[23]
Coronal heating problem
Why is the Sun’s corona (atmosphere layer) so much hotter than the Sun’s surface? Why is the magnetic reconnection effect many orders of magnitude faster than predicted by standard models?
Diffuse interstellar bands
What is responsible for the numerous interstellar absorption lines detected in astronomical spectra? Are they molecular in origin, and if so which molecules are responsible for them? How do they form?
Supermassive black holes
What is the origin of the M-sigma relation between supermassive black hole mass and galaxy velocity dispersion?[24] How did the most distant quasars grow their supermassive black holes up to 1010 solar masses so early in the history of the Universe?

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Can the discrepancy between the curves be attributed to dark matter?
Kuiper cliff
Why does the number of objects in the Solar System’s Kuiper belt fall off rapidly and unexpectedly beyond a radius of 50 astronomical units?
Flyby anomaly
Why is the observed energy of satellites flying by Earth sometimes different by a minute amount from the value predicted by theory?
Galaxy rotation problem
Is dark matter responsible for differences in observed and theoretical speed of stars revolving around the center of galaxies, or is it something else?
What is the exact mechanism by which an implosion of a dying star becomes an explosion?
Ultra-high-energy cosmic ray
[6] Why is it that some cosmic rays appear to possess energies that are impossibly high,given that there are no sufficiently energetic cosmic ray sources near the Earth? Why is it that (apparently) some cosmic rays emitted by distant sources have energies above the Greisen–Zatsepin–Kuzmin limit?[2][6]
Rotation rate of Saturn
Why does the magnetosphere of Saturn exhibit a (slowly changing) periodicity close to that at which the planet’s clouds rotate? What is the true rotation rate of Saturn’s deep interior?[25]
Origin of magnetar magnetic field
What is the origin of magnetar magnetic field?
Large-scale anisotropy
Is the Universe at very large scales anisotropic, making the cosmological principle an invalid assumption? The number count and intensity dipole anisotropy in radio, NRAO VLA Sky Survey (NVSS) catalogue[26] is inconsistent with the local motion as derived from cosmic microwave background[27][28] and indicate an intrinsic dipole anisotropy. The same NVSS radio data also shows an intrinsic dipole in polarization density and degree of polarization[29] in the same direction as in number count and intensity. There are other several observation revealing large-scale anisotropy. The optical polarization from quasars shows polarization alignment over a very large scale of Gpc.[30][31][32] The cosmic-microwave-background data shows several features of anisotropy,[33][34][35][36] which are not consistent with the Big Bang model.
Space roar
Why is space roar six times louder than expected? What is the source of space roar?
Age–metallicity relation in the Galactic disk
Is there a universal age–metallicity relation (AMR) in the Galactic disk (both “thin” and “thick” parts of the disk)? Although in the local (primarily thin) disk of theMilky Way there is no evidence of a strong AMR,[37] a sample of 229 nearby “thick” disk stars has been used to investigate the existence of an age–metallicity relation in the Galactic thick disk, and indicate that there is an age–metallicity relation present in the thick disk.[38][39] Stellar ages from asteroseismology confirm the lack of any strong age-metallicity relation in the Galactic disc.[40]
The lithium problem
Why is there a discrepancy between the amount of lithium-7 predicted to be produced in Big Bang nucleosynthesis and the amount observed in very old stars?[41]
Solar wind interaction with comets
In 2007 the Ulysses spacecraft passed through the tail of comet C/2006 P1 (McNaught) and found surprising results concerning the interaction of the solar wind with the tail.
Ultraluminous pulsar
The ultraluminous X-ray source M82 X-2 was thought to be a black hole, but in October 2014 data from NASA’s space-based X-ray telescope NuStar indicated that M82 X-2 is a pulsar many times brighter than the Eddington limit.
The injection problem
Fermi acceleration is thought to be the primary mechanism that accelerates astrophysical particles to high energy. However, it is unclear what mechanism causes those particles to initially have energies high enough for Fermi acceleration to work on them.[42]
Fast radio bursts
Transient radio pulses lasting only a few milliseconds, from emission regions thought to be no larger than a few hundred kilometers, and estimated to occur several hundred times a day. While several theories have been proposed, there is no generally accepted explanation for them. They may come from cosmological distances, but there is no consensus on this, either.[citation needed]
Nature of KIC 8462852
What is the origin of unusual luminosity changes of this star?
Fermi paradox
Do extraterrestrial civilizations exist? If so, why we do not see them?
Nature of Wow! signal
Was that a real signal and, if so, what is the origin of it?[43]

Nuclear physics

The “island of stability” in the proton vs. neutron number plot for heavy nuclei.

Quantum chromodynamics
What are the phases of strongly interacting matter, and what roles do they play in the evolution of cosmos? What is the detailed partonic structure of the nucleons? What does QCD predict for the properties of strongly interacting matter? What determines the key features of QCD, and what is their relation to the nature of gravity and spacetime? Doglueballs exist? Do gluons acquire mass dynamically despite having a zero rest mass, within hadrons? Does QCD truly lack CP-violations? Do gluons saturate[disambiguation needed] when their occupation number is large? Do gluons form a dense system called Color Glass Condensate? What are the signatures and evidences for the Balitsky-Fadin-Kuarev-Lipatov, Balitsky-Kovchegov, Catani-Ciafaloni-Fiorani-Marchesini evolution equations?
Nuclei and nuclear astrophysics
What is the nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes? What is the origin of simple patterns[which?] in complex nuclei? What is the nature of exotic excitations in nuclei at the frontiers of stability and their role in stellar processes? What is the nature of neutron starsand dense nuclear matter? What is the origin of the elements in the cosmos? What are the nuclear reactions that drive stars and stellar explosions?
Plasma physics and fusion power
Fusion energy may potentially provide power from abundant resource (e.g. hydrogen) without the type of radioactive waste that fission energy currently produces. However, can ionized gases (plasma) be confined long enough and at a high enough temperature to create fusion power? What is the physical mechanism of the transition from Low to High confinement scenarios?[44]

Atomic, molecular and optical physics

Abraham–Minkowski controversy
What is the momentum of photons in optical media?

Condensed matter physics

A sample of a cupratesuperconductor (specifically BSCCO). The mechanism for superconductivity of these materials is unknown.

High-temperature superconductors
What is the mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 25kelvin? Is it possible to make a material that is a superconductor at room temperature?[2]
Amorphous solids
What is the nature of the glass transition between a fluid or regular solid and a glassy phase? What are the physical processes giving rise to the general properties of glasses and the glass transition?[45][46]
Cryogenic electron emission
Why does the electron emission in the absence of light increase as the temperature of a photomultiplier is decreased?[47][48]
What causes the emission of short bursts of light from imploding bubbles in a liquid when excited by sound?[49][50]
Is it possible to make a theoretical model to describe the statistics of a turbulent flow (in particular, its internal structures)?[2] Also, under what conditions do smooth solutions to the Navier–Stokes equations exist? This problem is also listed as one of the Millennium Prize Problems in mathematics.
Alfvénic turbulence
In the solar wind and the turbulence in solar flares, coronal mass ejections, and magnetospheric substorms are major unsolved problems in space plasma physics.[51]
Topological order
Is topological order stable at non-zero temperature? Equivalently, is it possible to have three-dimensional self-correcting quantum memory?[52]
Fractional Hall effect
What mechanism explains the existence of the  u=5/2 state in the fractional quantum Hall effect? Does it describe quasiparticles with non-Abelian fractional statistics?[citation needed]
Bose–Einstein condensation
How do we rigorously prove the existence of Bose–Einstein condensates for general interacting systems?[53]

Magnetoresistance in a  u=8/5 fractional quantum Hall state.

Liquid crystals
Can the nematic to smectic (A) phase transition in liquid crystal states be characterized as a universal phase transition?[54][55]
Semiconductor nanocrystals
What is the cause of the nonparabolicity of the energy-size dependence for the lowest optical absorption transition of quantum dots?[56]
Electronic band structure
Why can band gaps not be calculated accurately?


Stochasticity and robustness to noise in gene expression
How do genes govern our body, withstanding different external pressures and internal stochasticity? Certain models exist for genetic processes, but we are far from understanding the whole picture, in particular indevelopment where gene expression must be tightly regulated.
Quantitative study of the immune system
What are the quantitative properties of immune responses? What are the basic building blocks of immune system networks? What roles are played by stochasticity?
What is the origin of the preponderance of specific enantiomers in biochemical systems?

Problems solved in recent decades

Existence of gravitational wave (1916-2016)
On 11 February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a pair of black holes merging,[57][58][59]which was also the first detection of a stellar binary black hole.
Perform a loophole-free Bell test experiment (1970[60]-2015)
In October 2015, scientists from the Kavli Institute of Nanoscience reported that the quantum nonlocality phenomenon is supported at the 96% confidence level based on a “loophole-free Bell test” study.[61][62] These results were confirmed by two studies with statistical significance over 5 standard deviations which were published in December 2015.[63][64]
Existence of pentaquarks (1964-2015)
In July 2015, the LHCb collaboration at CERN identified pentaquarks in the Λ0
channel, which represents the decay of the bottom lambda baryon (Λ0
into a J/ψ meson (J/ψ), a kaon (K−
and a proton (p). The results showed that sometimes, instead of decaying directly into mesons and baryons, the Λ0
decayed via intermediate pentaquark states. The two states, named P+
and P+
, had individual statistical significances of 9 σ and 12 σ, respectively, and a combined significance of 15 σ — enough to claim a formal discovery. The two pentaquark states were both observed decaying strongly to J/ψp, hence must have a valence quark content of two up quarks, a down quark, a charm quark, and an anti-charm quark (uudcc), making them charmonium-pentaquarks.[65]
Photon underproduction crisis (2014-2015)
This problem was resolved by Khaire and Srianand.[66] They show that a factor 2 to 5 times large metagalactic photoionization rate can be easily obtained using updated quasar and galaxy observations. Recent observations of quasars indicate that the quasar contribution to ultraviolet photons is factor 2 large as compared to previous estimates. The revised galaxy contribution is also factor 3 higher. This together solves the crisis.
Existence of ball lightning (1638[67]-2014)
In January 2014, scientists from Northwest Normal University in Lanzhou, China, published the results of recordings made in July 2012 of the optical spectrum of what was thought to be natural ball lightning made during the study of ordinary cloud–ground lightning on China’s Qinghai Plateau.[68][69] At a distance of 900 m (3,000 ft), a total of 1.3 seconds of digital video of the ball lightning and its spectrum was made, from the formation of the ball lightning after the ordinary lightning struck the ground, up to the optical decay of the phenomenon. The recorded ball lightning is believed to be vaporized soil elements that then rapidly oxidizes in the atmosphere. The nature of the true theory is still not clear.[69]
Higgs boson and electroweak symmetry breaking (1963[70]-2012)
The mechanism responsible for breaking the electroweak gauge symmetry, giving mass to the W and Z bosons, was solved with the discovery of the Higgs boson of the Standard Model, with the expected couplings to the weak bosons. No evidence of a strong dynamics solution, as proposed by technicolor, has been observed.
Hipparcos anomaly (1997[71]-2012)
The actual distance to the Pleiades – the High Precision Parallax Collecting Satellite (Hipparcos) measured the parallax of the Pleiades and determined a distance of 385 light years. This was significantly different from other measurements made by means of actual to apparent brightness measurement or absolute magnitude. The anomaly was due to the use of a weighted mean when there is a correlation between distances and distance errors for stars in clusters. It is resolved by using an unweighted mean. There is no systematic bias in the Hipparcos data when it comes to star clusters.[72]
Faster-than-light neutrino anomaly (2011-2012)
In 2011, the OPERA experiment mistakenly observed neutrinos appearing to travel faster than light. On July 12, 2012 OPERA updated their paper by including the new sources of errors in their calculations. They found agreement of neutrino speed with the speed of light.[73]
Pioneer anomaly (1980-2012)
There was a deviation in the predicted accelerations of the Pioneer spacecraft as they left the Solar System.[2][6] It is believed that this is a result of previously unaccounted-for thermal recoil force.[74][75]
Long-duration gamma ray bursts (1993[76]-2003)
Long-duration bursts are associated with the deaths of massive stars in a specific kind of supernova-like event commonly referred to as a collapsar. However, there are also long-duration GRBs that show evidence against an associated supernova, such as the Swift event GRB 060614.
Solar neutrino problem (1968[77]-2001)
Solved by a new understanding of neutrino physics, requiring a modification of the Standard Model of particle physics—specifically, neutrino oscillation.
Create Bose–Einstein condensate (1924[78]-1995)
Composite bosons in the form of dilute atomic vapors were cooled to quantum degeneracy using the techniques of laser cooling and evaporative cooling.
Cosmic age problem (1920s-1990s)
The estimated age of the universe was around 3 to 8 billion years younger than estimates of the ages of the oldest stars in the Milky Way. Better estimates for the distances to the stars, and the recognition of the accelerating expansion of the universe, reconciled the age estimates.
Nature of quasars (1950s-1980s)
The nature of quasars was not understood for decades.[79] They are now accepted as a type of active galaxy where the enormous energy output results from matter falling into a massive black hole in the center of the galaxy.[80]

See also


  1. Jump up^ Ginzburg, Vitaly L. (2001). The physics of a lifetime : reflections on the problems and personalities of 20th century physics. Berlin: Springer. pp. 3–200.ISBN 9783540675341.
  2. ^ Jump up to:a b c d e f Baez, John C. (March 2006). “Open Questions in Physics”. Usenet Physics FAQ. University of California, Riverside: Department of Mathematics. Retrieved March 7, 2011.
  3. Jump up^ “Alcohol constrains physical constant in the early universe”. Phys Org. December 13, 2012. Retrieved 25 March 2015.
  4. Jump up^ Bagdonaite, J.; Jansen, P.; Henkel, C.; Bethlem, H. L.; Menten, K. M.; Ubachs, W. (13 December 2012). “A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe”. Science 339 (6115): 46–48.Bibcode:2013Sci…339…46B. doi:10.1126/science.1224898.
  5. Jump up^ Podolsky, Dmitry. “Top ten open problems in physics”. NEQNET. Archivedfrom the original on 22 October 2012. Retrieved 24 January 2013.
  6. ^ Jump up to:a b c d e Brooks, Michael (March 19, 2005). “13 Things That Do Not Make Sense”. New Scientist. Issue 2491. Retrieved March 7, 2011.
  7. Jump up^ Steinhardt, P. and Turok, N. (2006). “Why the Cosmological constant is so small and positive”. Science 312: 1180–1183. arXiv:astro-ph/0605173.Bibcode:2006Sci…312.1180S. doi:10.1126/science.1126231.
  8. Jump up^ Alan Sokal (July 22, 1996). “Don’t Pull the String Yet on Superstring Theory”.New York Times
  9. Jump up^ Joshi, Pankaj S. (January 2009). “Do Naked Singularities Break the Rules of Physics?”. Scientific American
  10. Jump up^ Dirac, Paul, “Quantised Singularities in the Electromagnetic Field“.Proceedings of the Royal Society A 133, 60 (1931).
  11. Jump up^ Li, Tianjun; Dimitri V. Nanopoulos; Joel W. Walker (2011). “Elements of F-ast Proton Decay”. Nuclear Physics B 846: 43–99. arXiv:1003.2570.Bibcode:2011NuPhB.846…43L. doi:10.1016/j.nuclphysb.2010.12.014.
  12. Jump up^ Hansson, Johan (2010). “The “Proton Spin Crisis” — a Quantum Query” (PDF).Progress in Physics 3. Retrieved 14 April 2012.
  13. Jump up^ A. Blumhofer, M. Hutter (1997). “Family Structure from Periodic Solutions of an Improved Gap Equation”. Nuclear Physics B484: 80–96.Bibcode:1997NuPhB.484…80B. doi:10.1016/S0550-3213(96)00644-X.
  14. Jump up^ “India-based Neutrino Observatory (INO)”. Tata Institute of Fundamental Research. Retrieved 14 April 2012.
  15. Jump up^ Smarandache, Vic; Florentin Smarandache (2007). “Thirty Unsolved Problems in the Physics of Elementary Particles” (PDF). Progress in Physics 4.Bibcode:2009APS..HAW.KD010C.
  16. Jump up^ Nakamura (Particle Data Group), K; et al. (2010). “2011 Review of Particle Physics”. J. Phys. G 37 (7A): 075021. Bibcode:2010JPhG…37g5021N.doi:10.1088/0954-3899/37/7A/075021.
  17. Jump up^ Thomas Blum; Achim Denig; Ivan Logashenko; Eduardo de Rafael; Lee Roberts, B.; Thomas Teubner; Graziano Venanzoni (2013). “The Muon (g-2) Theory Value: Present and Future”. arXiv:1311.2198 [hep-ph].
  18. Jump up^ H. Muir (2 July 2003). “Pentaquark discovery confounds sceptics”. New Scientist. Retrieved 2010-01-08.
  19. Jump up^ G. Amit (14 July 2015). “Pentaquark discovery at LHC shows long-sought new form of matter”. New Scientist. Retrieved 2015-07-14.
  20. Jump up^ Laing, R. A.; Bridle, A. H. (2013). “Systematic properties of decelerating relativistic jets in low-luminosity radio galaxies”. arXiv:1311.1015 [astro-ph.CO].
  21. Jump up^ Strohmayer, Tod E.; Mushotzky, Richard F. (20 March 2003). “Discovery of X-Ray Quasi-periodic Oscillations from an Ultraluminous X-Ray Source in M82: Evidence against Beaming”. The Astrophysical Journal 586 (1): L61–L64. arXiv:astro-ph/0303665. Bibcode:2003ApJ…586L..61S. doi:10.1086/374732.
  22. Jump up^ Titarchuk, Lev; Fiorito, Ralph (10 September 2004). “Spectral Index and Quasi‐Periodic Oscillation Frequency Correlation in Black Hole Sources: Observational Evidence of Two Phases and Phase Transition in Black Holes” (PDF). The Astrophysical Journal 612 (2): 988–999. arXiv:astro-ph/0405360.Bibcode:2004ApJ…612..988T. doi:10.1086/422573. Retrieved 25 January2013.
  23. Jump up^ Shoji Kato (2012). “An Attempt to Describe Frequency Correlations among kHz QPOs and HBOs by Two-Armed Nearly Vertical Oscillations”. arXiv:1202.0121[astro-ph.HE].
  24. Jump up^ Ferrarese, Laura; Merritt, David (2000). “A Fundamental Relation between Supermassive Black Holes and their Host Galaxies”. The Astrophysical Journal 539: L9–L12. arXiv:astro-ph/0006053. Bibcode:2000ApJ…539L…9F.doi:10.1086/312838
  25. Jump up^ “Scientists Find That Saturn’s Rotation Period is a Puzzle”. NASA. June 28, 2004. Retrieved 2007-03-22.
  26. Jump up^ J J Condon, W D Cotton, E W Greisen, Q F Yin, R. A. Perley, G. B. Taylor, and J J Broderick.”The NRAO VLA Sky Survey”AJ, 115(5):1693-1716, May 1998.
  27. Jump up^ A. K. Singal. “Large Peculiar Motion of the Solar System from the Dipole Anisotropy in Sky Brightness due to Distant Radio Sources.”ApJL, 742:L23, December 2011.
  28. Jump up^ Prabhakar Tiwari, Rahul Kothari, Abhishek Naskar, Sharvari Nadkarni-Ghosh, Pankaj Jain. “Dipole anisotropy in sky brightness and source count distribution in radio NVSS data”.
  29. Jump up^ Prabhakar Tiwari and Pankaj Jain. “Dipole anisotropy in integrated linearly polarized flux density in NVSS data”.
  30. Jump up^ D. Hutsemékers “Evidence for very large-scale coherent orientations of quasar polarization vectors”A&A, 332:410-428, 1998.
  31. Jump up^ D. Hutsemékers and H. Lamy”Confirmation of the existence of coherent orientations of quasar polarization vectors on cosmological scales” A&A, 367(2):381-387, 2001.
  32. Jump up^ Pankaj Jain, Gaurav Narain, and S Sarala. “Large-scale alignment of optical polarizations from distant QSOs using coordinate-invariant statistics.”MNRAS, 347(2):394-402, 2004.
  33. Jump up^ Angélica de Oliveira-Costa, Max Tegmark, Matias Zaldarriaga, and Andrew Hamilton (2004). Significance of the largest scale cmb fluctuations in wmap. PhRvD, 69:063516.
  34. Jump up^ H.K. Eriksen, F.K. Hansen, A.J. Banday, K.M. Gorski, and P.B. Lilje. “Asymmetries in the Cosmic Microwave Background anisotropy field.”ApJ, 605:14–20, 2004.
  35. Jump up^ Pramoda Kumar Samal, Rajib Saha, Pankaj Jain, and John P. Ralston. “Testing Isotropy of Cosmic Microwave Background Radiation.”MNRAS, 385:1718, 2008.
  36. Jump up^ Pramoda Kumar Samal, Rajib Saha, Pankaj Jain, and John P. Ralston.”Signals of Statistical Anisotropy in WMAP Foreground-Cleaned Maps.”MNRAS, 396:511, 2009.
  37. Jump up^ Casagrande, L., et al. (2011) “New constraints on the chemical evolution of the solar neighbourhood and Galactic disc(s)“. Astronomy & Astrophysics, 2011, Volume 530, 138, 21 pp
  38. Jump up^ Bensby, T.; Feltzing, S.; Lundström, I. (July 2004). “A possible age-metallicity relation in the Galactic thick disk?”. Astronomy and Astrophysics 421 (3): 969–976.arXiv:astro-ph/0403591. Bibcode:2004A&A…421..969B. doi:10.1051/0004-6361:20035957.
  39. Jump up^ Gilmore, G.; Asiri, H.M. (00/2011). “Open Issues in the Evolution of the Galactic Disks“. Workshop on Gaia. Proceedings. Granada, ed. Navarro et al. 2011. Retrieved 2013-09-08.
  40. Jump up^ Casagrande, L., et al. (2016) “Measuring the vertical age structure of the Galactic disc using asteroseismology and SAGA“. MNRA, 2016, Volume 455, 987
  41. Jump up^ Brian D. Fields, The Primordial Lithium Problem
  42. Jump up^ André Balogh; Rudolf A. Treumann. “Physics of Collisionless Shocks: Space Plasma Shock Waves”. 2013. Section 7.4 “The Injection Problem”. p. 362.
  43. Jump up^ Futurism.com: “Tentatively finding even the most faint sign of extraterrestrial life would be the single most important discovery in the history of mankind, it could possibly help us find answers to the most existential mysteries of science(…)”
  44. Jump up^ F. Wagner (2007). “A quarter-century of H-mode studies”. Plasma Physics and Controlled Fusion 49: B1. Bibcode:2007PPCF…49….1W. doi:10.1088/0741-3335/49/12B/S01..
  45. Jump up^ Kenneth Chang (July 29, 2008). “The Nature of Glass Remains Anything but Clear”. The New York Times
  46. Jump up^ P.W. Anderson (1995). “Through the Glass Lightly”. Science 267 (5204): 1615.doi:10.1126/science.267.5204.1615-e. The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition.
  47. Jump up^ Cryogenic electron emission phenomenon has no known physics explanation. Physorg.com. Retrieved on 2011-10-20.
  48. Jump up^ Meyer, H. O. (1 March 2010). “Spontaneous electron emission from a cold surface”. EPL (Europhysics Letters) 89 (5): 58001. doi:10.1209/0295-5075/89/58001.
  49. Jump up^ Storey, B. D.; Szeri, A. J. (8 July 2000). “Water vapour, sonoluminescence and sonochemistry”. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 456 (1999): 1685–1709. doi:10.1098/rspa.2000.0582.
  50. Jump up^ Wu, C. C.; Roberts, P. H. (9 May 1994). “A Model of Sonoluminescence”.Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 445 (1924): 323–349. doi:10.1098/rspa.1994.0064.
  51. Jump up^ Goldstein, Melvyn L. (2001). “Major Unsolved Problems in Space Plasma Physics”. Astrophysics and Space Science 277 (1/2): 349–369.Bibcode:2001Ap&SS.277..349G. doi:10.1023/A:1012264131485.
  52. Jump up^ Yoshida, Beni (2011). “Feasibility of self-correcting quantum memory and thermal stability of topological order”. Annals of Physics 326 (10): 2566.arXiv:1103.1885. Bibcode:2011AnPhy.326.2566Y.doi:10.1016/j.aop.2011.06.001. Retrieved 8 April 2012.
  53. Jump up^ Schlein, Benjamin. “Graduate Seminar on Partial Differential Equations in the Sciences – Energy and Dynamics of Boson Systems”. Hausdorff Center for Mathematics. Retrieved 23 April 2012.
  54. Jump up^ Mukherjee, Prabir K. (1998). “Landau Theory of Nematic-Smectic-A Transition in a Liquid Crystal Mixture”. Molecular Crystals & Liquid Crystals 312: 157–164.doi:10.1080/10587259808042438. Retrieved 28 April 2012.
  55. Jump up^ A. Yethiraj, “Recent Experimental Developments at the Nematic to Smectic-A Liquid Crystal Phase Transition”, Thermotropic Liquid Crystals: Recent Advances, ed. A. Ramamoorthy, Springer 2007, chapter 8.
  56. Jump up^ Norris, David J. (2003). “The Problem Swept Under the Rug”. In Klimov, Victor.Electronic Structure in Semiconductors Nanocrystals: Optical Experiment (inSemiconductor and Metal Nanocrystals: Synthesis and Electronic and Optical Properties). CRC Press. p. 97. ISBN 9780203913260.
  57. Jump up^ Castelvecchi, Davide; Witze, Witze (February 11, 2016). “Einstein’s gravitational waves found at last”. Nature News. doi:10.1038/nature.2016.19361. Retrieved2016-02-11.
  58. Jump up^ B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016).“Observation of Gravitational Waves from a Binary Black Hole Merger”. Physical Review Letters 116 (6). doi:10.1103/PhysRevLett.116.061102.
  59. Jump up^ “Gravitational waves detected 100 years after Einstein’s prediction | NSF – National Science Foundation”. http://www.nsf.gov. Retrieved 2016-02-11.
  60. Jump up^ Philip M. Pearle (1970), “Hidden-Variable Example Based upon Data Rejection”,Phys. Rev. D 2 (8): 1418–25, doi:10.1103/PhysRevD.2.1418
  61. Jump up^ Hensen, B.; et al. (21 October 2015). “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres”. Nature 526: 682–686.doi:10.1038/nature15759. Retrieved 21 October 2015.
  62. Jump up^ Markoff, Jack (21 October 2015). “Sorry, Einstein. Quantum Study Suggests ‘Spooky Action’ Is Real.”. New York Times. Retrieved 21 October 2015.
  63. Jump up^ Giustina, M.; et al. (16 December 2015). “Significant-Loophole-Free Test of Bell’s Theorem with Entangled Photons”. Physical Review Letters 115: 250401.doi:10.1103/PhysRevLett.115.250401.
  64. Jump up^ Shalm, L. K.; et al. (16 December 2015). “Strong Loophole-Free Test of Local Realism”. Physical Review Letters 115: 250402.doi:10.1103/PhysRevLett.115.250402.
  65. Jump up^ R. Aaij et al. (LHCb collaboration) (2015). “Observation of J/ψp resonances consistent with pentaquark states in Λ0
    decays”. Physical Review Letters115 (7). arXiv:1507.03414. Bibcode:2015PhRvL.115g2001A.doi:10.1103/PhysRevLett.115.072001.
  66. Jump up^ Khaire and Srianand 2015, [1], MNRAS Letters,
  67. Jump up^ http://www.devonhistorysociety.org.uk/2009/10/widecombe-great-storm-1638.html
  68. Jump up^ Cen, Jianyong; Yuan, Ping; Xue, Simin (17 January 2014). “Observation of the Optical and Spectral Characteristics of Ball Lightning”. Physical Review Letters(American Physical Society) 112 (35001). Bibcode:2014PhRvL.112c5001C.doi:10.1103/PhysRevLett.112.035001. Retrieved 19 January 2014.
  69. ^ Jump up to:a b Ball, Philip (17 January 2014). “Focus: First Spectrum of Ball Lightning”.Focus (American Physical Society). Bibcode:2014PhyOJ…7….5B.doi:10.1103/Physics.7.5. Retrieved 19 January 2014.
  70. Jump up^ Higgs, Peter (2010-11-24). “My Life as a Boson” (PDF). Talk given by Peter Higgs at Kings College, London, Nov 24 2010, expanding on a paper originally presented in 2001. Retrieved 17 January 2013. – the original 2001 paper can be found at: Duff and Liu, ed. (2003) [year of publication]. 2001 A Spacetime Odyssey: Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics, Michigan, USA, 21–25 May 2001. World Scientific. pp. 86–88. ISBN 9812382313. Retrieved 17 January 2013.
  71. Jump up^ http://adsabs.harvard.edu/full/1999A%26A…341L..71V
  72. Jump up^ Charles Francis; Erik Anderson (2012). “XHIP-II: Clusters and associations”.arXiv:1203.4945 [astro-ph.GA].
  73. Jump up^ OPERA collaboration (July 12, 2012). “Measurement of the neutrino velocity with the OPERA detector in the CNGS beam”. arXiv:1109.4897 [hep-ex].
  74. Jump up^ Turyshev, S.; Toth, V.; Kinsella, G.; Lee, S. C.; Lok, S.; Ellis, J. (2012). “Support for the Thermal Origin of the Pioneer Anomaly”. Physical Review Letters 108 (24): 241101. arXiv:1204.2507. Bibcode:2012PhRvL.108x1101T.doi:10.1103/PhysRevLett.108.241101. PMID 23004253.
  75. Jump up^ Overbye, Dennis (23 July 2012). “Mystery Tug on Spacecraft Is Einstein’s ‘I Told You So’”. The New York Times. Retrieved 24 January 2014.
  76. Jump up^ C. Kouveliotou et al. Identification of two classes of gamma-ray bursts. Astrophys.J., 413:L101–104, 1993.
  77. Jump up^ http://iopscience.iop.org/article/10.1086/305343/fulltext/
  78. Jump up^ http://www.lorentz.leidenuniv.nl/history/Einstein_archive/
  79. Jump up^ “The MKI and the discovery of Quasars”. Jodrell Bank Observatory. Retrieved2006-11-23.
  80. Jump up^ Hubble Surveys the “Homes” of Quasars Hubblesite News Archive, 1996-35

External links

Unsolved Problems in Statistics

There are many longstanding unsolved problems in mathematics for which a solution has still not yet been found. The unsolved problems in statistics are generally of a different flavor; according to John Tukey,[1] “difficulties in identifying problems have delayed statistics far more than difficulties in solving problems.” A list of “one or two open problems” (in fact 22 of them) was given by David Cox.[2]

Inference and testing

Experimental design

Problems of a more philosophical nature


  1. Jump up^ Tukey, John W. (1954). “Unsolved Problems of Experimental Statistics”. Journal of the American Statistical Association (Journal of the American Statistical Association, Vol. 49, No. 268) 49 (268): 706–731. doi:10.2307/2281535. JSTOR 2281535.
  2. Jump up^ Cox, D.R. (1984) “Present position and potential developments: Some personal views — Design of experiments and regression”, Journal of the Royal Statistical Society, Series A, 147 (2), 306–315
  3. Jump up^ Nabendu Pal, Wooi K. Lim (1997) “A note on second-order admissibility of the Graybill–Deal estimator of a common mean of several normal populations”, Journal of Statistical Planning and Inference, 63 (1), 71–78. doi:10.1016/S0378-3758(96)00202-9
  4. Jump up^ Fraser, D.A.S.; Rousseau, J. (2008) “Studentization and deriving accurate p-values”. Biometrika, 95 (1), 1—16. doi:10.1093/biomet/asm093
  5. Jump up^ Jordan, M. I. (2011). “What are the open problems in Bayesian statistics?” The ISBA Bulletin, 18(1).
  6. Jump up^ Zabell, S. L. (1992). “Predicting the unpredictable”. Synthese 90: 205. doi:10.1007/bf00485351.


  • Linnik, Jurii (1968). Statistical Problems with Nuisance Parameters. American Mathematical Society. ISBN 0-8218-1570-9.
  • Sawilowsky, Shlomo S. (2002). “Fermat, Schubert, Einstein, and Behrens–Fisher: The Probable Difference Between Two Means When σ1 ≠ σ2“, Journal of Modern Applied Statistical Methods, 1(2).

We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all. But of course there is then no question left, and just this is the answer.

– Wittgenstein