Comments on: Another Clay Institute Millenium Prize Problem Solved?

Another Clay Institute Millenium Prize Problem Solved?

onalark — Thu, 05 Oct 2006 06:28:41 -0800

The Navier-Stokes equations constitute the fundamental equations that describe fluid mechanics, and are used everywhere from atmospheric science to airplane design. Proof of the existence of a smooth solution to the Navier-Stokes equations in 3-dimensions is considered a challenging problem, so challenging that the Clay Math Institute has offered a million dollars to anyone who can do so. Has it been done? (More detailed explanation). (via)

By: gleuschk

gleuschk — Thu, 05 Oct 2006 07:24:31 -0800

Wow. What a spectacular time for mathematics. (As a tiny bit of added spice, note that the "More detailed explanation" link is by Christina Sormani, who was a postdoc with Shing-Tung Yau, recently in the news. I don't know Sormani, but I tend to trust her description of Smith's work, just based on reputation.)

By: vernondalhart

vernondalhart — Thu, 05 Oct 2006 07:29:47 -0800

Oh my. Oh my indeed. Can this really be true?

By: noble_rot

noble_rot — Thu, 05 Oct 2006 08:16:00 -0800

Can epimorph please let me know whether the author is full of it? But I guess will find out soon enough, as I'm sure every scholar of real analysis is pouring over this as we speak.

By: mr_roboto

mr_roboto — Thu, 05 Oct 2006 11:20:39 -0800

Wow. This would be very, very big.

By: delmoi

delmoi — Thu, 05 Oct 2006 11:27:58 -0800

That's pretty damn impressive. I thought that the equation was actually proven to be unsolvable.

By: jcruelty

jcruelty — Thu, 05 Oct 2006 15:31:24 -0800

no way!! first the Poincaré Conjecture and now this. odds that someone finds a flaw in her proof? anybody intimate with state of the art in PDEs?

By: intermod

intermod — Thu, 05 Oct 2006 20:06:46 -0800

I consider it one of my lifetime crowning acheivements that I managed to understand the Navier-Stokes equations enough to get my aerospace engineering degree. A degree which turned out to be useless for me*, but hey it's fun to point to sometimes. Not that I remember any of that stuff, mind you ... Gawd, that LaTex look in the paper is so HOT. Written by a woman. I'm about to swoon. * Hey, YOU try to get an AE job during the post Cold War defense contraction period in the early 90s while competing against laid-off Rockwell guys with 35 years of experience. Oh and I had a 2.4 GPA. Woooooo!

By: spazzm

spazzm — Fri, 06 Oct 2006 04:49:22 -0800

Gawd, that LaTex look in the paper is so HOT. LaTex is nerd-speak for "Hey, check out my Big Brain!"

By: casarkos

casarkos — Fri, 06 Oct 2006 06:36:22 -0800

Does this mean I can go back and complain to my aerodynamics professor now?

By: jcruelty

jcruelty — Fri, 06 Oct 2006 11:51:01 -0800

i haven't seen any updates... what's the dilly?

By: onalark

onalark — Fri, 06 Oct 2006 13:59:58 -0800

i haven't seen any updates... what's the dilly? The 'dilly', my friend, is that mathematics professors highly trained in this field will be pouring over her research for years before a decision is made. Although her proof is 9 pages, this is the final link in probably more than a decade's worth of work for her (as evidenced by all the referenced publications).

By: gleuschk

gleuschk — Sat, 07 Oct 2006 07:40:39 -0800

I got a pleasant note from Christina Sormani, asking me to make sure two things are clear: 1. She hasn't claimed to have checked Smith's work on the webpage linked in the post, just to provide an exposition which will help those involved in the verification process (which will likely take years). 2. She was a postdoc with S.-T. Yau back in the 90s, and is now on the faculty at CUNY. It's "poring", not "pouring".

By: gleuschk

gleuschk — Sun, 08 Oct 2006 15:59:36 -0800

The paper has been withdrawn.

By: onalark

onalark — Mon, 09 Oct 2006 09:29:06 -0800

Thanks for the update gleuschk.

By: onalark

onalark — Mon, 09 Oct 2006 18:21:34 -0800

One of my analysis friends said something about one of her results leading to a contradiction, so there's some sort of discrepancy in her proof (which would explain the withdrawl). Well it was a good bit of excitement anyway, and I'm hoping she'll be able to correct the error.

By: gleuschk

gleuschk — Tue, 10 Oct 2006 05:58:39 -0800

There's a fair amount of new information on Christina Sormani's page linked in the original post. The surprising thing about the retraction is that the error was found in one of Smith's papers that had already been refereed, accepted for publication, and had even appeared in print. That sort of thing isn't supposed to happen. Generally speaking, the author always holds the final responsibility for the correctness of his/her results, but if I were the referee for the previous paper, I'd be pretty damn embarrassed about now.

By: intermod

intermod — Fri, 27 Oct 2006 05:50:49 -0800

There's some followup about the withdrawal in this SlashDot post -- 4th item down.