Talk:Millennium Prize Problems

Undecidable?

Is the prize only awarded for showing that the conjectures are true or false, or does one also claim the prize for showing that a conjecture cannot be proven via the axioms? —Preceding unsigned comment added by 86.153.11.178 (talk) 19:50, 24 January 2011 (UTC)

It is all prone to attack and very well all problems in the set are solved in a single swipe

http://meami.org/

This is the html version of the file http://claymath.org/library/monographs/MPPc.pdf. Google automatically generates html versions of documents as we crawl the web.

<...WP:COPYVIO material removed by User:EdJohnston. See below...>

—Preceding unsigned comment added by 204.128.192.4 (talk) 05:50, 12 May 2010 (UTC)

The material originally posted by the IP editor above comes from a PDF file that is still available online from the web site of the Clay Mathematics Institute. http://www.claymath.org/library/monographs/MPP.pdf, whose home page is at http://www.claymath.org. Verbatim reproduction of this file on Wikipedia surely violates their copyright, so I've deleted it from this talk page. Our readers should consult the original PDF file instead. EdJohnston (talk) 19:28, 29 June 2010 (UTC)

Millennium Prize Problems Conditions

"Only the Poincaré conjecture has been solved, but the solver has not pursued the conditions necessary to claim the prize." What exactly are these conditions?

EDIT: [the french article says] the solution must be widely accepted by the mathematical community for two years after publication before the Millennium Prize is given away.

The conditions to be awarded the prize are generally given as three stages. Above is 'stage 2'.

1-"Before consideration, a proposed solution must be published in a refereed mathematics publication of worldwide repute..."

2-"..and it must also have general acceptance in the mathematics community two years after."

3-The science advisory board of the Clay Mathematics Institute appoints a panel to inspect the problem and make a report and recommendation the the directors of the Institute who in turn have the final say in awarding the prize.

{info from the book Poincares Prize by George G Szpiro} Zybthranger (talk) 00:20, 7 October 2008 (UTC)

thanks, but the perelman article states that "he has yet to be offered the prize," meaning that it seems only to be a matter of time. Twipley (talk) 16:05, 9 February 2009 (UTC)

Navier Stokes

I was told during my time at grad school that the rules were changed so that giving a counter example existence and uniqueness for Navier Stokes problem specifically was not sufficient to win the prize. Is this officially the case? Thenub314 (talk) 16:10, 21 January 2009 (UTC)

In the case of the P versus NP problem and the Navier-Stokes problem, the SAB will consider the award of the Millennium Prize for deciding the question in either direction. In the case of the other problems if a counterexample is proposed, the SAB will consider this counterexample after publication and the same two-year waiting period as for a proposed solution will apply. If, in the opinion of the SAB, the counterexample effectively resolves the problem then the SAB may recommend the award of the Prize. If the counterexample shows that the original problem survives after reformulation or elimination of some special case, then the SAB may recommend that a small prize be awarded to the author. The money for this prize will not be taken from the Millennium Prize Problem fund, but from other CMI funds.

Never mind their rules are clear enough about counter examples. Thenub314 (talk) 16:16, 21 January 2009 (UTC)

Copyright issues

The entire lead of this article is found verbatim at http://www.claymath.org/millennium/ and there may be more within the content. The article needs some review as to these matters. My76Strat (talk) 00:04, 1 June 2010 (UTC)

Copyright problem removed

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P vs NP

I have removed the references to Deolalikar's briefly-claimed proof, since, following many flaws found in the community, he has removed all mention of the draft paper from his web page. I know that at least one of the other MPs had a briefly claimed proof, later withdrawn, so clearly there is no intention to record all such here. Should a corrected version appear, then of course it should be mentioned here, but currently that seems vanishingly unlikely.Educres (talk) 21:57, 10 August 2010 (UTC)

What if Riemann Hypothesis is Baseless?

Riemann Hypothesis is baseless, where it can neither be true nor false. http://www.gsjournal.net/Science-Journals/Essays/View/4491 — Preceding unsigned comment added by 112.134.176.24 (talk) 19:35, 30 January 2013 (UTC)

Declined in 2010?

"but he declined the award in 2010" - That's unsourced, and I know for a fact it's incorrect - I read about him declining the award while I was still in college, and I graduated in 2009. It must have happened around 2008 or 2009, definitely not 2010. BlueRaja (talk) 00:06, 11 March 2013 (UTC)

The prize was not even offered until 2010. See [1]. Roger (talk) 04:21, 12 March 2013 (UTC)

He declined the Fields medal in 2006. You may have been thinking of that. 50.0.121.102 (talk) 21:16, 23 January 2014 (UTC)

P = NP Solved by Physics Trick

What do you think of the use of a fact from physics to sove a mathematics problem? As v approaches c, NP computational scaling factors approach polynomial ones, for example, if x is the amount of data to be calculated and it can require either x^2 time (or rate) or x! time, then using Relativity in the form of the Twin Paradox:

x! / x^2 = (1- v^2 / c^2)^0.5

Solving for v:

v = c (1 - (x^2 / x!)^2

Albert deBroglie (talk) 23:55, 1 September 2013 (UTC)

This is discussed a little in section 6 of Scott Aaronson's article "NP-complete problems and physical reality".[2] Aaronson and Watrous have another paper saying that in a computational model allowing computing in closed timelike curves (from general relativity), PSPACE becomes tractable.[3] The formal P vs NP problem just counts the number of steps performed in the calculation though: physical time distortions don't change that. 50.0.121.102 (talk) 21:22, 23 January 2014 (UTC)

Navier-Stokes

There's a new paper by Otelbaev purporting to solve NS, that's currently mentioned in this article both in the NS section and in the lede. The paper seems to be getting a fairly subdued reception in the math world, so I'm about to take it out of the lede but leave it in the NS section. If anyone really feels differently, feel free to put it back. 50.0.121.102 (talk) 21:55, 23 January 2014 (UTC)