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Another Millenium Problem May Have Been Solved134

S3D writes "After recent verification of the proof of the Poincaré conjecture, another of the Clay Institute's Millenium Problems may have been solved. This new solution is for Navier-Stokes equations under physically reasonable conditions. Navier-Stocks equations describe the motion of fluid substances such as liquids and gases. Penny Smith has posted an Arxiv paper entitled 'Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System' which may prove the existence of such solutions."
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Another Millenium Problem May Have Been Solved

• I solve 3 millennium problems before breakfast (Score:3, Insightful)

on Saturday October 07, 2006 @04:40AM (#16346137) Homepage
Well, at least contributors to arXiv between them seem to. (The 'GM' section in mathematics has been dubbed by some serious mathematicians "garbage machine", for example.)

Wait for the peer review to begin. I've not seen anyone familiar with the field say anything about the paper yet, only then does it gain credibility.

FatPhil
• Re:What is the geometry? (Score:1, Insightful)

by Anonymous Coward on Saturday October 07, 2006 @07:48AM (#16346865)
Caveat: Though I started out in CFD I have not read CFD papers for some 12 years. and frankly I dont understand much of the math in this paper.

That's OK - this is slashdot.

Most commenters won't have even read the article, let get as far as failing to understand it!

• Re:Neat indeed (Score:5, Insightful)

on Saturday October 07, 2006 @11:22AM (#16348287)

Not necessarily -- it is conceivable that there exists a poly-time algorithm for an NP-complete problem, but there is no proof (within ZFC, say) that it is correct. The physical truth is certain -- but what we can know about the physical truth is limited.

Now, I'm with you in believing that that's extraordinarily improbable, but math doesn't always respect what we consider to be likely.

In my opinion (as a complexity theory grad student), the "maybe P=NP is independent" speculation is bunk. There are genuine, interesting results talking about the limits of how we can resolve P vs. NP, but none of them come anywhere near logical independence, and giving up on a field-defining problem after 30-odd years is just very odd considering how long the really major open problems often take to solve. I believe the solution exists, and I hope it is found soon, but I will be unsurprised if it takes another 100 years or so while we get a better handle on what computation really means.

• Re:Someone had better tell the Formula One teams (Score:2, Insightful)

on Saturday October 07, 2006 @11:38AM (#16348389)
Using the Finite Element Method (FEM) will give you very good results. I've worked with Comsol and Floworks simulations designing a variety of things - but mostly cooling loops. This is where the problem lies - these simulations are very computer intensive and even a simple simulation such as a cooling loop through copper (one bend) can take over a day to converge to a solution (and i would make all sorts of assumptions to cut the time down, like perfectly smooth walls). A desktop computer wouldn't even be able to handle a more realistic simulation of the same loop. So the problem isn't with our knowledge of teh equations or the algorithms, it's a lack of available computer power. It turns out it's easier to build a wind tunnel than a supercomputer.

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