Talk:Unsolved problems in mathematics

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

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.


Here are some more external links to unsolved problems pages. I'm not really sure about external link etiquette. Some of these reference each other. I've just picked out some of the most interesting. Let me know what you think about adding these links to the article. --noösfractal 07:54, 3 August 2005 (UTC)

Contents

[edit] 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:

  • 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.

Any thoughts or comments (even "looks fine") would be appreciated. CRGreathouse (t | c) 02:35, 7 November 2006 (UTC)

From SergioLerner:

[edit] 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)

[edit] 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

  • seen the light
  • died
  • spent so little effort trying to understand the problem that we can reclassify them as "don't really care."

Tom Duff 17:51, 7 February 2007 (UTC)

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

[edit] 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.....

[edit] 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)

[edit] 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)

[edit] Modeling black hole mergers

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