Talk:List of unsolved problems in mathematics/Archive 1

Poincaré Conjecture
Can't we move Poincaré Conjecture to solved problems, since it was even awarded the Fields Medal? Ricbit 20:30, 25 August 2006 (UTC)

Impossible problems
For the lay reader, its useful to distinguish these from problems known to be impossible of solution, e.g. squaring the circle. And Gödel's incompleteness theorem is similarly worth mentioning.

Prizes offered
It might be useful (indeed motivational) if somebody added a table listing all of the monetary and reoutational prozes offered for the solution of each of the problems. Clay's 1,000,000$ prizes are quite popular, but some other, such as the Beal conjecture's (100,000$), are less known. This could help foster research into these areas. — Preceding unsigned comment added by Aswarp (talk • contribs) 14:47, 3 December 2014 (UTC)


 * This is a nice idea. I think a good starting point to get references for this would be this question on MathOverflow Saung Tadashi (talk) 21:37, 21 December 2014 (UTC)

Categories
The list is starting to get long, so I tried to break it up into general categories. I did this pretty quickly; I'd like to have someone else look this over before converting these from comments to subheadings. In particular: Any thoughts or comments (even "looks fine") would be appreciated. CRGreathouse (t | c) 02:35, 7 November 2006 (UTC)
 * Are the problems in the right categories?
 * Is there a better grouping for the problems in "Other"?
 * What do you think of my division of number theory? I have it in three parts: primes, additive number theory, and general number theory.
 * Should any of the current categories be divided or subsumed into others? I don't think I broke it down too small, but perhaps combinatorics or Ramsey theory could be combined somewhere.  In the other direction, number theory could perhaps be split further.

From SergioLerner:

The definition of "Unsolved Problem"
What's the definition of "Unsolved Problem"? If someone creates a new problem that cannot solve, one or two persons work on it a couple of hours and cannot not solve it either.. Is it already an "Unsolved problem"?. Does it have to be published and some time past to be called "Unsolved"?

Until that question is answered I added the Pollock octahedral numbers conjecture and the Lerner octahedral numbers conjecture (both of them are only two years old now). --Sergiolerner 15:08, 5 February 2007 (UTC)

Four-color Theorem
The article contains the claim "Some do not accept the proof [of the four-color theorem] because it is heavily based on computer computation." This was certainly the case in 1977. But is it still true, thirty years later? Surely everyone who originally thought this has either Tom Duff 17:51, 7 February 2007 (UTC)
 * seen the light
 * died
 * spent so little effort trying to understand the problem that we can reclassify them as "don't really care."

Apparently I'm the only one that cares about this, so I'm making the change. Tom Duff 00:20, 3 March 2007 (UTC)

Unsolved/Recently solved problems
This article about unsolved problems in mathematics has a section about recently solved problems and now also a list of books about recently solved problems. Do these belong here? I suggest to put these into a separate article on recently solved or famous solved mathematical problems. What do you think? — Ocolon 17:49, 14 March 2007 (UTC)

I would disagree with this last comment. Knowing whether or not a recently popular "unsolved problems" has, in actuality, been recently solved would save a lot of hassle for the amateur mathematician. But.....

THE "Problems solved recently" HAVEN'T been Computationally Verified.
If one looks at the work of, say, C. Paulson : http://www.cl.cam.ac.uk/users/lcp/papers (I've seen some of his work, and it looks 'deep' - for example, his proof of Sylow's Theorem via the use of the Isabelle/HOL automated theorem prover), it is clear that there are mathematical problems whose proofs should be verified via automated theorem provers. This should be done as even peer-review can easily overlook real and important proof-flows. In particular, I believe that the METAMATH (www.metamath.org) theorem prover seems to be 'the best'. It enables automatic proof verification from the ZFC axioms upwards.

THE BASIC POINT I AM ESSENTIALLY ATTEMPTING TO MAKE, IS THAT THERE ARE LARGE BODIES OF MATHEMATICAL KNOWLEDGE THAT HAVE BEEN ACCEPTED AS TRUE DUE TO PEER-REVIEW, BUT WHICH HAVE NOT BEEN AUTOMATICALLY CHECKED VIA THE USE OF AUTOMATED THEOREM PROVING UTILITIES, ETC...

This is unfortunate - human beings make mistakes quite often, though computers tend to be more reliable. It could be argued that humans program computers, so that computers are no less fallible than their creators/programmers. However, this ignores the fact that humans can create simple software (such as compilers/automated theorem provers) that enable the compilation/proof verification of code/proofs that have a complexity several orders of magnitude greater than said compilers/automated theorem provers.

Again, I should repeat this point, doesn't a proof like that of Fermat's Last Theorem feel like a House of Cards a little too tall to be taken for granted without at least SOME attempts at Automated Proof Verification?

ConcernedScientist 00:12, 31 May 2007 (UTC)
 * This is all very interesting, even in all upper-case, but this is not the place for this discussion. There must be lots of forums out there where people discuss this sort of thing: talk pages are for the discussion of the improvement of the associated articles.  Cheers, Doctormatt 01:02, 31 May 2007 (UTC)

Graph isomorphism problem
I didn't understand this entry. I suspect the question is whether the problem is in P or NP-complete? (It may be neither or both). If this interpretation is correct, why does it feature in combinatorics and not in complexity theory (which maybe doesn't belong to Maths but to Computer Science, but then so does P=NP). --Thorsten 23:44, 30 October 2007 (UTC)
 * I'm removing it as unclear. Feel free to re-add it with a precise statement of what it ought to mean. Algebraist 15:42, 17 February 2008 (UTC)

Modeling black hole mergers
Is there a formulation of "modeling black hole mergers" that looks anything remotely like an unsolved problem in mathematics?&mdash;GraemeMcRaetalk 23:14, 31 December 2007 (UTC)

Problems in Topology
Seems like some problems in Topology are important enough to be included. The smooth Poincare conjecture and the 11/8 conjecture come to mind as examples. 67.169.47.149 (talk) 08:45, 20 November 2008 (UTC)

Dates
Would be nice to have some references in this problem list, especially giving dates for when the problem was first stated in the given form. For example, it looks like the oldest problem here is the existence of odd perfect numbers? Is that right? best, Sam nead (talk) 20:07, 31 January 2009 (UTC)

what about...
Set theory and mathematical logic are conspicuously missing.  Grue  07:44, 25 May 2009 (UTC)

Value of the sofa constant
Would the moving sofa problem be notable enough for inclusion in this article? – Acdx (talk) 15:25, 18 August 2009 (UTC)


 * Absolutely! I heard of it when I were a teenager, so I would consider it notable! —Preceding unsigned comment added by Paxinum (talk • contribs) 20:39, 18 August 2009 (UTC)


 * Free feel to add it if you can figure out which category it falls under.. – Acdx (talk) 14:46, 19 August 2009 (UTC)

Khabibullin’s conjecture on integral inequalities
Is "Khabibullin’s conjecture" an established prase? Is it mentioned in scholarly papers? Kope (talk) 13:34, 17 April 2010 (UTC)
 * Thanks for the many answers. It will take some time to read all of them. Kope (talk) 13:00, 23 April 2010 (UTC)

Is sum of reciprocals of primes under a googolplex less than 8?
This question was added as an unsolved problem. Before I revert it, let me first point out that according to Proof that the sum of the reciprocals of the primes diverges, the sum of reciprocals of primes less than n is at least ln(ln(n+1))-ln(pi^2/6), and a googolplex is 10^(10^100), so the sum of reciprocals of the primes under a googolplex is ln(ln(10^(10^100)+1))-ln(pi^2/6) ~= 230.595. So it's not an unsolved problem at all. Is the subject of the unsolved problem a googol, rather than a googolplex?&mdash;GraemeMcRaetalk 17:13, 27 May 2010 (UTC)
 * In the absence of citations, and seeing as this is a an arbitrary problem of limited mathematical value, I removed the item. Feel free to add it back of relevant sources are found and notability can be established. Owen&times; &#9742;  18:23, 27 May 2010 (UTC)
 * Now we have a new, but equally boring, question, which I reverted. Is the sum of reciprocals of primes under a googol less than 6?  The answer is yes, because this sum is a little over ln(ln(10^100))-ln(pi^2/6), which is about 4.94.&mdash;GraemeMcRaetalk 00:19, 2 July 2010 (UTC)
 * Although it's probably very close to the actual sum, you are using a lower bound for the sum when you, instead, need an upper. So the question, "Is the sum of reciprocals of primes under a googol less than 6?", is not resolved by this argument; we only know that it's not less than ~4.94. In any case, the question does not belong in the article w/o proper citation. Justin W Smith talk/stalk 02:04, 2 July 2010 (UTC)
 * I suspect that any upper bound for the sum would specify a value more than 6, so the question might really be unsolved. But obviously, unsolved alone is not sufficient reason for inclusion in this article. Justin W Smith talk/stalk 02:15, 2 July 2010 (UTC)

For which n can we find n different odd positive integers such that the sum of their reciprocals is 1?
For which n can we find n different odd positive integers such that the sum of their reciprocals is 1? —Preceding unsigned comment added by 83.130.105.91 (talk) 14:57, 22 January 2011 (UTC)


 * Thanks for not putting your question back in the article. If no one answers you here, try the Reference Desk. Rivertorch (talk) 15:04, 22 January 2011 (UTC)

n-body problem
A thread at Talk:list of unsolved problems in physics reckons that finding a closed form for a solution to the n-body problem(or disproving that such a form exists) is a problem in mathematics not physics. It's an important problem, one of the oldest unsolved problems around, and for me should be listed somewhere, but where it would go on this page I don't know, as currently the only physical mathematics problems on this page are (correct me if I'm wrong) Navier-Stokes and Yang-Mills, which of course are in their own special section. —Preceding unsigned comment added by 82.6.96.22 (talk) 21:20, 4 March 2011 (UTC) The boundary between physics and mathematics is not that clear the n-body problem should be listed in this article. — Preceding unsigned comment added by 2601:7:E80:678:18AB:6B66:B8A0:499D (talk) 20:07, 9 June 2015 (UTC)

Surface of constant width.
http://en.wikipedia.org/wiki/Surface_of_constant_width has a link to this article but here it isn't any citation to that problem.--79.109.46.149 (talk) 16:07, 31 August 2011 (UTC)

Schoolboy solves which 2 of these problems ?
Hi, I notice that this google search brings up a group articles that say a schoolboy just solved 2 dynamics/ballistics problems that Isaac Newton set - I was trying to find an article to update and any information on the solution. anyone know whether there are articles on the problems? EdwardLane (talk) 08:55, 27 May 2012 (UTC)
 * It appears that there is a related article Shouryya Ray EdwardLane (talk) 11:14, 28 May 2012 (UTC)
 * I have yet to see anything other than newspaper stories about this, and the newspaper stories have very little content. &mdash; Carl (CBM · talk) 11:40, 28 May 2012 (UTC)
 * Just inserting a quote from Boud that he wrote on the talk page from Shouryya Ray which seems relevant.EdwardLane (talk) 15:58, 28 May 2012 (UTC)
 * BCrowell on slashdot suggests that the problem could be wikisource:The Mathematical Principles of Natural Philosophy (1846)/BookII-I or wikisource:The Mathematical Principles of Natural Philosophy (1846)/BookII-II and that Shouryya's solution is $$g^2/(2u^2)+(\alpha g/2)[v \sqrt{u^2+v^2} / u^2 + \mathrm{arsinh} |v/u|] = \mathrm{const}$$, maybe corresponding to the 2D case. Boud (talk) 19:36, 27 May 2012 (UTC)

Euler equations
Under Differential equations, an unsolved problem is "Regularity of solutions of Euler equations".

However, there are many types of Euler equations. It's ambiguous which one the article refers to. Glyph27notfound (talk) 00:34, 14 November 2012 (UTC)

No proven impossibilities?
I came here at least hoping for a list of proven impossibilities to be linked in see also, alas is there even such an article on WP? — Preceding unsigned comment added by 97.114.64.28 (talk) 11:57, 28 July 2013 (UTC)

Are these listed problems real?
Under the section Number theory (prime numbers) the following two problems are listed (with references, which I've omitted here): Now, I cannot find the first problem in its reference and the reference for the second problem is not accessible to me. But these problems seem so simple that I suspect they aren't real. For if we take a=3 in the first problem, we can show that there are no solutions (which also answers the second problem). Any power of a=3 will produce an odd number. A prime p squared is always an odd number (except if p=2, but that case can be easily distinguished and excluded), so to satisfy 1 (mod p2), the number must be even. Since any power of 3 is odd, it will never satisfy this, and therefore there is no prime p such that 3p &minus; 1 ≡ 1 (mod p2). (Or am I saying something stupid?) Hrothberht (talk) 10:21, 9 November 2014 (UTC)
 * Are there for every a ≥ 2 infinitely many primes p such that ap &minus; 1 ≡ 1 (mod p2)?
 * Can a prime p satisfy 2p − 1 ≡ 1 (mod p2) and 3p − 1 ≡ 1 (mod p2) simultaneously?


 * I believe there is a mistake in the statement "so to satisfy 1 (mod p2), the number must be even". For instance, 310 ≡ 1 (mod 112). Saung Tadashi (talk) 15:34, 9 November 2014 (UTC)
 * Yes, you're right. So I was saying something stupid. Hrothberht (talk) 21:37, 9 November 2014 (UTC)
 * It can happen to anyone. The most important is to always try to make Wikipedia better, as you had intended :)   Best regards, Saung Tadashi (talk) 01:40, 10 November 2014 (UTC)

Merger proposal
Due to the similarity between the name of the articles and since this article has the section "Books discussing unsolved problems", I propose that Lists of unsolved problems in mathematics be merged into List of unsolved problems in mathematics. Saung Tadashi (talk) 20:11, 24 December 2014 (UTC)
 * Support merge. The "lists of" article is short, some of it is already here, and this article could benefit from a discussion of older lists of problems that are not all still unsolved (notably Hilbert's list). I don't see a good rationale for keeping them separate. —David Eppstein (talk) 20:34, 24 December 2014 (UTC)


 * Merged. Saung Tadashi (talk) 17:49, 15 January 2015 (UTC)

Geometry/Task packaging
What is the direction of the smallest square in which you can package 2 unit circle, one of which is allowed to cut the chord on the 2nd segment? The above geometric task of packing for me is solved. Prompt please where it is possible to represent the solution and the proof of fidelity to solve this problem. 93.81.44.163 (talk) 17:33, 29 January 2015 (UTC)

Multiple issues template
I removed the templates for resolved issues  because of the nice recent edit by Rick Norwood. Hermel (talk) 21:38, 25 March 2015 (UTC)

Partial differential equations
The link for 'Regularity of solutions of Euler equations' under the topic partial differential equations doesn't work correctly and links to a page of equations named after Euler. — Preceding unsigned comment added by 121.223.137.91 (talk) 12:03, 21 May 2015 (UTC)

Statement = Problem ?
It seems to be assumed in many places in this article and other articles in Wikipedia that it is obvious for some statements that they are problems. I guess that in those cases the problem is to prove that the statement is true or that it is false. I think I can understand why mathematicians have come to think that it is a given that some statements are obvious in this sense. I do not think it is reasonable to assume that the normal reader of Wikipedia understands this. Am I missing something? --Ettrig (talk) 15:19, 27 August 2015 (UTC)

Recent revert
Someone reverted my addition of the Fluid section citing that I added reference links instead of problems. Every unsolved problem need not have a clean neat name ending with fancy hypothesis, conjecture or problem. Two physics related Millennium problems (with far fewer interwiki links, presumably because of this) also fall in this category. So it is not possible to answer "What are the unsolved problems" unless you write down the whole statement of the problems which runs afoul with our copyvio rules. The other option is to completely avoid anything related to Mathematical Physics and Fluid Mechanics which seems, atleast to me, very unfortunate.

So what is the harm to provide direct links to lists compiled by recognized experts in the field (for physics related themes) which also saves us from WP:OR trouble? Solomon7968 05:57, 31 January 2016 (UTC)
 * Are you seriously seeking to defend your edits, which among other sins included an entire line copied-and-pasted without credit from somebody's conference schedule web page (and uselessly context-free here)? —David Eppstein (talk) 06:41, 31 January 2016 (UTC)
 * No I am defending the idea that for some aforementioned fields adding expert-compiled lists is a better approach than adding nothing/WP:OR-laden wall of problems. The reason for including the line you say is that I am trying to locate an Internet version of the Fefferman lecture (that's moot anyway because it's preserved permanently in page history, in case I forget it later). Solomon7968 06:54, 31 January 2016 (UTC)
 * Your re-revert of my addition (along with ce) deserves explanation. I will go further to suggest that we completely reorganize the entire remaining list adding expert-compiled lists to each of the sub disciplines. If we can't find such lists for enough sub disciplines they can be kept in an external link section. If you can't justify why those can't be kept in any manner in the article I suggest you self revert. Solomon7968 18:14, 31 January 2016 (UTC)
 * I have reverted, twice now, because your addition is totally off-topic for this list. If you want a list of collections of open problems, that should be a different article. It should be obvious that that's not what this one is about. If you want to use the references you found to source actual open problems in fluid dynamics, go ahead, but that's not what you did. It's clear that you haven't even digested some of the things you are listing because one of them (not there in your second attempt) was a talk announcement copied from a web site, with no evidence that the talk itself was recorded and is available. As for your suggestion that I should just go away and leave you to cruft up the article: no. And I won't tell you to go away yourself, either, because really, what I would prefer is that you get better at judging what content is appropriate to add to articles. —David Eppstein (talk) 04:47, 1 February 2016 (UTC)
 * I said above to either justify your revert or to do self revert. Next time you write a reply about something I simply didn't suggested, I will call you a liar. My question remains about what objection you have about something which I did indeed suggested: "that we completely reorganize the entire remaining list adding expert-compiled lists to each of the sub disciplines. If we can't find such lists for enough sub disciplines they can be kept in an external link section"?
 * Other watchers of this article are also welcome to comment, of course. Let us see if they consider this material totally off-topic. Solomon7968 11:15, 1 February 2016 (UTC)

Leap year
Can anybody solve the leap year issue as all the gods fails by 24 hours Mickydma (talk) 04:12, 1 February 2016 (UTC)

Who proved the Geometrization Conjecture?
The section on proven problems since 1995 emphasizes Morgan and Tian as having "completed the proof" of the Geometrization Conjecture based on "the work of Perelman." I checked this against the page for the Geometrization Conjecture itself and it gives exclusive emphasis to Perelman while adding later that several groups (including Morgan and Tian) added proofs for a Theorem that Perelman stated but didn't prove himself. It's a bit odd to put such emphasis onto Morgan and Tian when Perelman seems to have been the chief architect of the proof by far...and of course the politics involved seemed to be a sensitive issue for him and many others. Let the man have his achievement. It's fine to say that others clarified things he said, but don't put them first and act as though Perelman is an afterthought or springboard. 24.190.214.204 (talk) 17:01, 19 April 2016 (UTC)

Mathematical Physics
I added a link to a list compiled on Mathematical Physics by Michael Aizenman. Among others it has mention of the Navier–Stokes existence and smoothness problem, contributed by Yakov Sinai. This list might be of possible interest to researchers working on this problem to see where the problems fits in the larger context of Mathematical Physics.

One question that comes to my mind is why Charles Fefferman was chosen to deliver the official statement of the problem ignoring Sinai. If he previously published anything related to the NS equations then it might be worth adding to his bio. Solomon7968 15:31, 6 May 2016 (UTC)

Hadwiger conjecture
The Hadwiger Conjecture in Graph Theory is listed twice. The second of these should be deleted, as it does not summarize the conjecture.24.85.118.113 (talk) 18:50, 20 September 2016 (UTC)
 * ✅. Thanks for catching this. —David Eppstein (talk) 19:01, 20 September 2016 (UTC)

Hadwiger conjecture
The Hadwiger Conjecture in Graph Theory is listed twice. The second of these should be deleted, as it does not summarize the conjecture.24.85.118.113 (talk) 18:50, 20 September 2016 (UTC)
 * ✅. Thanks for catching this. —David Eppstein (talk) 19:01, 20 September 2016 (UTC)

Topology
Why is there no section for problems in topology? — Preceding unsigned comment added by 31.221.90.4 (talk) 13:44, 25 November 2016 (UTC)

Four Landau Problems should be individually listed
They are hugely important and iconic: Goldbach's conjecture: Can every even integer greater than 2 be written as the sum of two primes? Twin prime conjecture: Are there infinitely many primes p such that p + 2 is prime? Legendre's conjecture: Does there always exist at least one prime between consecutive perfect squares? Are there infinitely many primes p such that p − 1 is a perfect square? They can be cross-ref'd as "one of Landau's Problems".

— Preceding unsigned comment added by 173.9.89.229 (talk) 17:43, 10 April 2017 (UTC)

Games and Puzzles
This note has been in the article of this section and I support including it to make article encyclopedic:
 * (See also Unsolved games)

2600:1700:6E40:FF0:C2C:68E7:2123:2A13 (talk) 06:52, 31 July 2018 (UTC)
 * The fact that it has been in the article before means nothing, and making the article "encyclopedic" is too vague to be an argument. Please be more specific. XOR&#39;easter (talk) 13:23, 2 August 2018 (UTC)

Indef-blocked user editing "Games and puzzles"
Someone indefinitely blocked for sockpuppetry is remarkably insistent upon adding a link to Solved game in the "Games and puzzles" section of this list. When I say remarkably, this is what I mean:
 * 

The edit summaries are repetitive and never really make a case for the change, despite multiple editors (User:Joel B. Lewis, User:David Eppstein and myself) reverting it. Above and beyond the block-evasion issue, I don't find the addition worthwhile on its own merits. This page is already just barely on the manageable side of miscellaneous, and indiscriminately linking to things that are tangentially related is not a helpful course of action. (The blocked editor insists on being "comprehensive", but so did the librarians of Babel.) Unless we have documentary evidence that math people are treating the solution of a mathematical game as a mathematical problem and writing about it in mathematics journals, then it doesn't belong on this list. XOR&#39;easter (talk) 16:22, 4 April 2019 (UTC)
 * And again. XOR&#39;easter (talk) 21:32, 5 April 2019 (UTC)
 * The page should be semi-protected. Maybe could do that? D.Lazard (talk) 21:47, 5 April 2019 (UTC)
 * I filed an SPI more than a week ago and it has received 0 attention so far :(. --JBL (talk) 22:02, 5 April 2019 (UTC)
 * Given that I've been one of the ones reverting, I should probably not also be the one to protect it, per WP:INVOLVED. —David Eppstein (talk) 22:08, 5 April 2019 (UTC)
 * I have submitted a request at WP:RPP. D.Lazard (talk) 22:20, 5 April 2019 (UTC)
 * The page has been semiprotected three months by User:El C due to the WP:RPP request. I am marking the SPI for close because there doesn't seem to be anything else that admins can do. Let me know if the same person starts editing more articles as part of their campaign. EdJohnston (talk) 16:11, 6 April 2019 (UTC)

Milestone
Every item now has a bluelink, a reference or both. XOR&#39;easter (talk) 16:15, 7 April 2019 (UTC)
 * Thanks for completing this! It would be nice if every item also had a short gloss, but that will be a lot more work. —David Eppstein (talk) 18:03, 7 April 2019 (UTC)
 * At least it's the kind of big job that can be done in small pieces. XOR&#39;easter (talk) 22:10, 8 April 2019 (UTC)
 * The current redlinks in the list: Taniyama's problems, Unsolved Problems on Mathematics for the 21st Century, DARPA's math challenges, Hartshorne conjectures, MNOP conjecture, Zariski multiplicity conjecture, Kung–Traub conjecture, Closed curve problem, Calluna's Pit, Birkhoff conjecture, Quantum unique ergodicity conjecture, Guralnick–Thompson conjecture, density hypothesis, Keating–Snaith conjecture, and Mazur's conjectures. In the "solved since 1995" list, we have Erdős sumset conjecture, Babai's problem, Anderson conjecture, Beck's 3-permutations conjecture, Kauffman–Harary conjecture, Normal scalar curvature conjecture, Böttcher–Wenzel Conjecture, Nirenberg–Treves conjecture, Alon–Friedgut conjecture, Kirillov's conjecture, Kouchnirenko’s conjecture, Deligne's conjecture on 1-motives, Erdős–Stewart conjecture and Harary's conjecture. Some of these could be articles, and some could conceivably be redirects to (sections of) existing pages, while perhaps some should be trimmed completely. I don't have strong feelings about what the inclusion criteria should be. On the other hand, a few sections seem awfully short, "group theory" and "topology" in particular. XOR&#39;easter (talk) 22:56, 9 April 2019 (UTC)

Calluna's Pit
I am puzzled by the inclusion of this problem. Unless I am misinterpreting its statement, this does not seem to be an unsolved problem. E.g. The Rectilinear Crossing Number of a Complete Graph and Sylvester's “Four Point Problem” of Geometric Probability appears to give a solution in theorem 1. The number does appear to be different than that given by Douglas Reay's page, so perhaps I am misinterpreting the statement. Perhaps or  care to correct my interpretation? Eigenbra (talk) 14:47, 11 April 2019 (UTC)
 * I agree. Also the reference (to an old web page of mine that merely links to the original "Calluna's pit" web page, to the paper above, and to another deadlink) is not a good choice. This appears to be based on a misunderstanding: the original "Calluna's pit" web page did not know of the significant body of research on the problem under a different name. I think it should be removed. —David Eppstein (talk) 16:13, 11 April 2019 (UTC)
 * Done. XOR&#39;easter (talk) 16:51, 11 April 2019 (UTC)

Inclusion criteria for the list of recent(-ish)ly solved problems?
While investigating the redlinks in this list, I looked up the Erdős–Stewart conjecture, but pretty much all I could find was what I added to my sandbox page here. I don't think there's enough to warrant an article, and I'm not sure that a result which would at most be a section in a larger page should be represented here. Otherwise, we'd be encompassing most of the math papers published in the last quarter-century.... Where and how should we draw the line? XOR&#39;easter (talk) 17:04, 11 April 2019 (UTC)
 * Relatedly, what should be done with problems that are actually a family of problems? E.g. the hypersphere packing problem is listed as an unsolved problem. The 3D case (Kepler's conjecture) is listed in the recently solved section. The 8D and 24D versions, solved more recently, are not yet listed. Similar situations re:Ramsey numbers, kissing numbers, etc. Eigenbra (talk) 19:01, 11 April 2019 (UTC)
 * That's a good question. I guess I'm fine with including a problem in both lists, if the partial solution was itself a big step forward. XOR&#39;easter (talk) 15:17, 12 April 2019 (UTC)

Toeplitz' conjecture
This is mentioned twice. Once as Inscribed square problem and another time as Toeplitz' conjecture. -Abdul Muhsy (talk) 13:46, 15 August 2019 (UTC)
 * Thanks, I have merged the two into a single entry, including both names. --JBL (talk) 14:23, 15 August 2019 (UTC)
 * Good catch, thanks! XOR&#39;easter (talk) 14:49, 15 August 2019 (UTC)

Ordinal analysis
The page is locked, but one should add questions in ordinal analysis. In particular,
 * What is the proof-theoretic ordinal of strong theories such as full second-order arithmetic or  ZF and ZFC?

Btw. "model theory and formal languages" is a pretty coarse section title. Maybe it can eventually be broken up. Proper logic questions like those of arithmetic in second order logic aren't just model theory and have no real place to go on the list.

Ordinal analysis
The page is locked, but one should add questions in ordinal analysis. In particular,
 * What is the proof-theoretic ordinal of strong theories such as full second-order arithmetic or  ZF and ZFC?

Btw. "model theory and formal languages" is a pretty coarse section title. Maybe it can eventually be broken up. Proper logic questions like those of arithmetic in second order logic aren't just model theory and have no real place to go on the list.

Ordinal analysis
The page is locked, but one should add questions in ordinal analysis. In particular,
 * What is the proof-theoretic ordinal of strong theories such as full second-order arithmetic or  ZF and ZFC?

By the way, "model theory and formal languages" is a pretty coarse section title. Maybe it can eventually be broken up. Proper logic questions like those of arithmetic in second order logic are not just model theory and have no real place to go on the list right now. (93.83.185.90 (talk) 17:11, 22 September 2019 (UTC))
 * Please supply reliably published sources for any questions you think should be added. Not everything here is properly sourced but that doesn't mean we should make that problem worse. —David Eppstein (talk) 18:50, 22 September 2019 (UTC)


 * I think a recent overview of what was achieved so far is the one below. ZF is the far out end, we're not even close.
 * "The Art of Ordinal Analysis" by Rathjen, https://www1.maths.leeds.ac.uk/~rathjen/ICMend.pdf
 * 91.112.18.90 (talk) 18:44, 12 October 2019 (UTC)

Pages included in category, but not page.
I noticed there were a few pages in the "Unsolved problems in mathematics" category that aren't included in the actual list.

Most notably:

Hermite's problem (algebraic number theory)

The Bing-Borsuk conjecture (topology)

Tarski's exponential function problem (model theory)

The question of "is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as the sums of three cubes?"

Should these be included? — Preceding unsigned comment added by GalacticShoe (talk • contribs) 17:37, 18 October 2019 (UTC)


 * Also Connes embedding problem in von Neumann algebra theory. 73.168.5.183 (talk) 05:40, 19 January 2020 (UTC)

On the status of Vaught's conjecture
It seems Vaught's conjecture is still open, since the community has no consensus on Knight's counterexample:

https://mathoverflow.net/questions/22142/has-vaughts-conjecture-been-solved

And Prof. Knight is still updating his counterexample:

https://people.maths.ox.ac.uk/knight/stuff/preprints.html

I think we should remove Vaught's conjecture from the solved problem list.

--Shiyu Ji (talk) 00:17, 13 April 2020 (UTC)
 * I agree. I think it's significant that a recent paper "Three red herrings around Vaught's conjecture" (TAMS 2016) doesn't even mention Knight's supposed counterexample. (I found this searching for Knight and Vaught, but it turns out that the Knight they mention is Julia not Robin.) —David Eppstein (talk) 01:18, 13 April 2020 (UTC)

Poincaré conjecture not solved in all dimensions for smooth category
The article states:

"The seventh problem, the Poincaré conjecture, has been solved."

It has been solved in the topological category in all dimensions. It has been resolved that PL and smooth homotopy spheres in all dimensions are topologically spheres. As the article correctly states, the smooth Poincaré conjecture is not settled in dimension 4.

But it neglects to mention that the corresponding smooth Poincaré conjecture has not been resolved in all dimensions! For instance, it is known that all smooth structures on a sphere of dimensions 1, 2, 3, 5, 6, 12, or 61 are diffeomorphic to the standard sphere. But it is not known whether there are any higher dimensions with this property.50.205.142.50 (talk) 21:37, 6 May 2020 (UTC)

Semi-protected edit request on 12 June 2020
Mathematics of an world 106.197.174.98 (talk) 02:48, 12 June 2020 (UTC)
 * ❌ No specific change requested. XOR&#39;easter (talk) 02:53, 12 June 2020 (UTC)

Semi-protected edit request on 29 October 2020
Organise the Problems solved since 1995 section of the page by subject in the same way the List of unsolved problems in physics page does it as shown here. 73.168.5.183 (talk) 03:35, 29 October 2020 (UTC)
 * The page is not protected, so you are free to update it. – Thjarkur (talk) 13:44, 29 October 2020 (UTC)
 * Huh, guess I must have missed something. Last few times I came to this page it was semi-protected — Preceding unsigned comment added by 73.168.5.183 (talk) 20:04, 29 October 2020 (UTC)
 * The semi-protection apparently expired in July. (I'd forgotten about it and haven't kept track.) XOR&#39;easter (talk) 20:08, 29 October 2020 (UTC)

reversion because dearth is thought better
David Eppstein because WP:CS "A citation, also called a reference,[note 1] uniquely identifies a source of information" the wikilinks are references that identify the source of the information - i.e. the individuals are the sources; I'll concur with the reverting user @ "history" with regards to the years

1. The article title doesn't indicate the list shouldn't include the information of the individuals who created the conjectures and problems and the years the problems were created, especially as a matter of comparison, the Millenium problems table shows the same information that was just reverted.

2.I can't support removing the information because of the obvious flaw in your criticism as I already indicated, shown copied at the beginning to this topic heading

3. the only reason I could think of as of why you would have wanted to remove the content is to cause the list to be the most simple viewable version, but this minimalization of information is only tantamount to providing a list of skulls of people (for example like found in an archaeology discovery) - but the meaning of the thing we are looking at, either the skull of an ancient hominid, for example, or a mathematical problem - both are only a mystery in the first view without any clues as to how to identify the thing - without the names, it isn't possible to orientate within the article, the viewer has to navigate away then return to this article then re-navigate if they would want to know how the particular problem or conjecture is caused to have the name that it has. Also having a skull for example, the names of the conjectures being likes archaeology skulls, lets say, as a route to think about this problem, having the skull, without any suggestion of the skull containing a brain, or the skull being attached to a body, that is a living version of an object (in archaeology there wouldn't be such a thing, because there are multi-disciplinary aspects to comprehending a subject - why you think a simply-only-list is sufficient for understanding?

4. I do agree the list looks less appealing with more information, and confuses the conjectures, problems, etc - i.e. including the individuals and years does create a problem with the article - but that doesn't devalue the individuals or years

5. "This article has been rated as List-Class on the project's quality scale" doesn't support any improving direction at all to the article, as the rate has no position, perhaps the article should be re-assessed...

with regards, Autonomous agent 5 (talk) 23:56, 18 June 2021 (UTC)
 * The context: Autonomous agent 5 has been going through adding to each entry names and dates of people who posed the problem or worked on it or had it named for them despite not actually working on it or something like that. My strong feeling is that this list is the wrong place for that kind of information, because we lack the space to go to more than one line per problem, because the history of most of these problems has too much nuance to be crammed into a single line, because claims about the history require sources and AA5's changes were unsourced, and because some random mathematician's name is rarely the first thing one wants to know about these problems anyway. Instead we should be focusing on providing a concise (one line) description of the problem, a link to the article where the history and other information can be properly recounted, and a footnote reference to the problem being unsolved. Too many of the entries here are unsourced, and that's a much bigger problem than these edits did nothing to repair. (PS your ping didn't work because they don't work when you add them later instead of in your initial message.) —David Eppstein (talk) 01:12, 19 June 2021 (UTC)
 * well actually that was a presumption, as I chose the individuals who created the conjectures, problems, etc at every entry - i.e. as the reason for my response @ 22:51, 18 June 2021, with regards to  "WP:CS "A citation, also called a reference...identifies a source of information" the wikilinks are references that identify the source of the information - i.e. the individuals are the sources " in response to your critique/indication "... We need wikilinks to problems and references to those problems...", so I don't see how it's possible  "...or had it named for them despite not actually working on it or something like that..some random mathematician's name.." since the connection of the debated links here is mostly obvious (for the majority, with peoples names as identifiers) at a cursory viewing by seeing the name as being the same as the identifier existing listed - I think you've presumed I represent the usual disappointment/chagrin that you (and others) experience of others non-appreciation for what is needed in life here...but annoyingly, I suppose, I think mostly it's obvious what the basic skeleton of information necessary is, to most people - so there isn't really anything for us to disagree on (is what I'm trying to state) - really I think we agree on the subject and some ulteriorly motivated other non-participating factor is a divisive influence on our mutual forwarding of the article - particularly since I agree also with "a concise (one line) description of the problem". But also I think currently your perception is at fault/in error "a link to the article where the history and other information can be properly recounted" already partly exists, the listed links in this current version show the connexion to the creating individuals (i.e. the "history" and in some cases the years of creation of conjecture, problem etc - as these connected articles are where I sourced the links which we debate here. Autonomous agent 5 (talk) 13:42, 19 June 2021 (UTC)

Erdős distinct distances problem
This page lists the Erdős distinct distances problem as having been solved by Guth and Katz in 2011, but on the page for the problem itself, it is listed as having instead been nearly solved in 2015. As I'm not an expert in this (or, to be quite honest, any) field of maths, I was wondering if someone could comment on or, if erroneous, fix this discrepancy? GalacticShoe (talk) 19:52, 19 June 2021 (UTC)
 * The date discrepancy is probably merely the usual difference between when the result was first announced and when it finally made it through the publication process. Or did you mean the part about how there is still a much smaller sqrt-log gap between the upper and lower bounds? —David Eppstein (talk) 19:58, 19 June 2021 (UTC)
 * Hello Prof. Eppstein, thank you very kindly for the prompt reply; I believe the difference between announcement and publication definitely covers the date discrepancy, but another concern I had (and my apologies for the grammatical ambiguity) was the usage of the word 'almost' within the article (incorrectly quoted by me as 'nearly' above.) Would you happen to know if this is because some aspect of the problem has not been proven, or if this is a mistake in the article's part; if the former, should it still be included within the problems solved category? Thanks for your time. GalacticShoe (talk) 20:24, 19 June 2021 (UTC)

1995?
The section, "Problems_solved_since_1995" (https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Problems_solved_since_1995) should begin with at least a brief explanation of why 1995 is being used as a starting point for documentation. I think it's ok if the reasons are somewhat arbitrary, but they should be explained. Perhaps this was just a few years prior to when some editor decided to begin cataloging problems that were notably unsolved and now solved? DKEdwards (talk) 05:36, 23 September 2021 (UTC)


 * Not really an explanation per se, but from what I can tell from the edit history, the section was originally for problems solved starting from 1975, and it was changed to 1995 since there were only three problems listed as solved between 1975 and 1995 (the Bieberbach conjecture, finding an optimal strategy for the princess and monster game, and the four color theorem), which was felt to be too few problems to merit having that stretch of time be included. To that extent you could argue that it starts from 1995 mostly because from that point onward, that's when a lot of results can be collectively thought of as proofs of famous conjectures rather than just results in their own right (at the very least, I don't think that proofs of long-standing problems just suddenly started ramping up in 1995.) I personally like it as a starting date because of Wiles's proof of FLT, which I'd argue is a result particularly well-known and regarded as profound, and thus, a worthy marker to begin with, year-wise, but of course that's just a personal opinion. GalacticShoe (talk) 13:46, 23 September 2021 (UTC)

Bad authors etc
has noticed a lot of garbage in the references. It seems that this was (mostly?) caused in this edit by User:Citation bot in November 2018. I don't know if this represents human error, robot error, a recurring problem, .... --JBL (talk) 13:52, 1 December 2021 (UTC)

Solved problems
I have a couple of questions in re some of the solved problems listed.

1. The Vaught conjecture is listed as having been solved, and indeed a counterexample/disproof was announced or published by Robin Knight in 2002; however, it is also stated that said counterexample/disproof has not yet been verified. As such, I was wondering if it is still fair to include it as being solved (at the very least, is it widely believed that the counterexample/disproof is valid?)

2. The Sidon set problem is listed as having been solved by J. Cilleruelo, I. Ruzsa and C. Vinuesa in 2010, but the result is not mentioned in the wiki page and there is no indication on said page of whether or not the problem solved in 2010 is indeed the "main" Sidon sequence problem. Can anyone confirm what the specific result proved is and whether or not the Sidon sequence page needs to be updated?

GalacticShoe (talk) 21:49, 27 December 2021 (UTC)


 * To 1., there is a similar question about the status of the Vaught conjecture in the archive for this Talk page (from 2020) if you aren't already aware. Joel Brennan (talk) 04:16, 9 March 2022 (UTC)

André–Oort conjecture is proved without RH
Yep. Valery Zapolodov (talk) 19:24, 6 February 2022 (UTC)