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Archive 1

Why are these Millennium Prize Problems so hard to solve?

Can anyone explain, to a non-mathematician, why these 7 hypotheses are so difficult to prove wrong/right? What is the part that is hard? Proving them by for example "induction" or something like that?

Hi there. These are some of the most important problems at the cutting-edge of maths research (really technical maths at that); that's generally why they are so hard to solve. MP (talk) 19:42, 20 January 2007 (UTC)

And cant computers just calculate like 10 billion values and see if they are correct and then assume all values are?  :)

Semi-exhaustive verification of a hypothesis (for example, by checking 10 billion values) is not the same as mathematical proof. The same goes for science - just because all known observations say something about our universe (for example, that protons, neutrons and electrons are the ultimate building blocks of matter), that does not mean to say that some future observations will not contradict these old observations - it just increases the probability of the hypothesis being true, but doesn't necessarily preclude something else being true (namely, that quarks are more fundamental, for example). In the same way, checking a statement for 10 billion or so values certainly increases the probability of the statement being true, but to clinch it, a rigorous proof must be provided - this is what maths is about. Hope this helps. MP (talk) 19:42, 20 January 2007 (UTC)

What does this mean?

"the board is integrated by members of the Clay family" - what does this mean?

I guess someone had maths on their mind when they wrote that. I replaced it with something more coherent Chenxlee (talk) 18:25, 13 February 2008 (UTC)

DeBranges

I would like some clairification about the so-called "apology" by DeBranges, who claims (I think) that he has solved the Riemann conjecture. Did he? Is he claiming the prize? Why would Karl Sabbagh in his book, The Riemann Hypothesis, devote eight pages of real mathematics to it in a popular book intended for non-mathematicians? The eight pages in Sabbagh's book don't look like a proof of anything to me, although the mathematics presented there looks extremely interesting. So it doesn't look as if DeBranges is nuts.Why haven't we seen something in the press? Whats' going on?

ambiguous wording...

In the following paragraph (from the article), the last statement ("whether a given equation even has any solutions") is ambiguous. Should it perhaps read "it was proven that there is no way to decide whether a given equation has any solutions at all." ?

If you know, go ahead and fix it - thanks.


The Birch and Swinnerton-Dyer conjecture


The Birch and Swinnerton-Dyer conjecture deals with a certain type of equation, those defining elliptic curves over the rational numbers. The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. Hilbert's tenth problem dealt with a more general type of equation, and in that case it was proven that there is no way to decide whether a given equation even has any solutions.

my removal of de Branges info from RH section

My edit summary was perhaps not the clearest here. I removed the part mentioning the de Branges claim to have proven the Riemann Hypothesis because I felt it was inappropriate. Generally we should keep these short descriptions to descriptions of the problems and avoid mentioning speculation; the most significant can be mentioned in the main article on the problem. In the case of the Poincare conjecture, the difference is that there is consensus that Perelman has proven it. So it would certainly be worth mentioning something, as someone reading this page might otherwise mistakenly think the problem is widely considered open. On the other hand, I wouldn't object to removing the Perelman info either, as it is not yet established fully through verifiable channels. --C S (Talk) 22:39, 10 April 2006 (UTC)

Separate articles ?

Would it be better to have separate articles on the Clay Mathematics Institute (CMI) and the Millennium Prize Problems (MPP)? Although there is a close link, the institute itself is clearly distinct from the establishment of the problems, which is why I think that the redirect from MMP to CMI is silly. The millenium prize problems can be discussed at leisure in more detail in such a new article, whilst this article should keep the current section title 'The Millenium Prize Problems' and briefly discuss the fact that there are these seven problems and their significance, but have a main article link to the MMP article. Thoughts on this ? MP (talk) 19:15, 8 May 2006 (UTC)

I almost agree with you, except that if you separated out the millennium problems the CMI article would be rather short. Write some more material about the other activities of CMI and then I'll support the split. —Keenan Pepper 01:10, 9 May 2006 (UTC)
It's a good point that the prizes and institute are separate; however, I don't see the need for the problems to be discussed in more detail. It seems to me that the separate articles on the problems are the place for that, and the brief descriptions on the current article are sufficient. --C S (Talk) 07:06, 9 May 2006 (UTC)

I agree with Keenan Pepper that if more can be written about the CMI, then a split would be better. As for discussing the problems in more detail in a new article MPP, I can see both sides of the coin now. Ok, it's not necessary to discuss the individual problems in more detail (as these are already discussed in the relevant articles), but I think that a general discussion of the problems and their significance (in maths and physics) can be mentioned, as well as attempts at solving them. It may not be a very long article, but the attempt at solving the Millennium Prize Problems are still in their infancy and a general discussion will undoubtedly expand over time, thus lengthening the article. In fact, for better organisation of articles and their content, it may be better to not even mention the individual problems in the CMI article (which should have a section on the MPP and a main article link to MPP, where the problems are mentioned and discussed with the 7 main article links). MP (talk) 19:47, 13 May 2006 (UTC)

A link to the QEDen wiki was added to the external links section some time ago. When I took a look, I found a wiki that is not very active: not all the problems have active participants, and the ones that do seem to consists of a small amount of discussion by just a few people. The wiki seems to have gotten some publicity, e.g. on Slashdot, but I don't see the benefit of having a link to it. It appears neither that popular or informative. If anyone has a reason for keeping it, please speak up. --C S (Talk) 07:18, 9 May 2006 (UTC)

It looks to me like qeden.com is no longer the millenium problems wiki. But then I can't read Japanese. Joee92 (talk) 00:14, 21 September 2009 (UTC)

Hilbert's Problems reference

I don't have sufficient maths background yet to resolve this issue myself, but the reference to Hilbert's problems, but the line that says "Of the initial twenty-three Hilbert problems, the only one which is still unsolved (or unproven) is the Riemann hypothesis, which was formulated in 1859 and is today one of the seven Millennium Prize Problems" seems inconsistent with the article on [Hilbert's problems], which seems to show that a number of them are open or unresolved. Anybody with better knowledge care to look into this? —The preceding unsigned comment was added by Maelin (talk • contribs) 12:51, 10 May 2006 (UTC)

This was brought up almost two months ago and hasn't yet been answered, so I'm guessing this is the incorrect page and changing it. —Simetrical (talk • contribs) 02:19, 23 May 2006 (UTC)

Grigori Perelman's proof and Millenium Prize

I know that he refused the Fields medal, but what about the Millenium Prize? Which of the following is true:

  • Grigori Perelman refused it, either. (When it was granted to him? When did he refuse it? Did somebody try and convince him to accept the money?)
  • He was found ineligible to win the prize (why? when?)
  • The issue is not solved yet (why? when it will be solved?)

It is strange that this article says nothing about the issue. --Urod 05:11, 9 February 2007 (UTC)

Proposed articles

Regarding splitting the articles (see above), I believe it is high time to do so. Consequently, I have proposed a replacement to the Clay Mathematics Institute article:

The MMP have to go somewhere, and my proposal is the following:

I would appreciate comments on these proposals. Thanks. MP (talk•contribs) 10:55, 16 October 2007 (UTC)

Looks great. Leave the article The out from the title. —Keenan Pepper 20:27, 16 October 2007 (UTC)
Further to the above comments, I've replaced the CMI article with a shorter version and created Millennium Prize Problems. MP (talk•contribs) 19:04, 17 October 2007 (UTC)

resignations?

Did Jaffe et al rercently resign from the institute?130.86.14.65 (talk) 05:29, 13 February 2008 (UTC)

current president?

Is he Nick Woodhouse (and not James Carlson as pointed in article)? — Preceding unsigned comment added by Vp loreta (talk • contribs) 08:35, 5 September 2012 (UTC)

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