Navier&Stokes to follow Poincare?

[neutrino]

Navier&Stokes to follow Poincare??

It seems that yet another important problem in mathematics, and more importantly in physics, may have been solved. This time it's the Navier-Stokes Equation. This, too, is on the Clay Mathematical Institute's list of Millenium Problems. I've seen a couple of blog entries in the past week on this, so here are all the links...


Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System[/url][Arxiv]

http://www.claymath.org/millennium/Navier-Stokes_Equations/

http://www.math.columbia.edu/~woit/wordpress/?p=470
http://asymptotia.com/2006/10/05/update-on-the-giant-killers/

Obviously, I can't make head or tail of all this, so the pros here can decide whether it's worthy enough of the award.

To the mods: I've posted this in General Math section based on the author's choice in the Arxiv.

 

[arildno]

WOW!
If this holds true, then it is a great advance.

I'll try to get a head of this, but I'm not sure if I manage to attach its tail properly.

Thanks, neutrino!

 

[CRGreathouse]

Yeah, I called my local newspaper yesterday to see if they wanted to run a note mentioning this.

 

[desA]

Did they understand you?

 

[fourier jr]

when i looked at that columbia blog page one of the last comments said pennny's paper had been 'withdrawn'. the person didnt say what was wrong with the proof but it looks like 'false alarm'... for now.

 

[neutrino]

Thanks for that, Fourier jr. Looking at the arxiv link, one can see that it has gone through a few revisions in the past week.

 

[Karlisbad]

Did anyone tried the proposed proof of RH ?

http://arxiv.org/abs/math.GM/0607095

 

[CRGreathouse]

Did anyone tried the proposed proof of RH ?

That looks like quasi-math by someone who doesn't know TeX.

 

[Karlisbad]

That looks like quasi-math by someone who doesn't know TeX.

You can't judge a book by its cover... if you were "ugly" would yo like to be judged by your physical aspect?.

Of course i have read by didn't understand most of it, at least i think the author is trying to say us that the "Trace" of the operator [tex] Tr(u)=e^{iu\hat H} [/tex] exists and is related to the derivative of a certain numer-theory function, and that the potential satisfies (as seen on the wikipedia)

[tex] Tr(u)u^{1/2}\sim \int_{-\infty}^{\infty}dxExp(iuV(x)+0.25i\pi) [/tex]

 

[waht]

"Authors: Penny Smith
Comments: Withdrawn
Subj-class: Differential Geometry; Analysis of PDEs
MSC-class: 35Qxx

This paper is being withdrawn by the author due a serious flaw. "


Looks like false alarm.

 

[matt grime]

Of course i have read by didn't understand most of it, at least i think the author is trying to say

It is going to take some convincing for me to believe that you are not Jose. Every post you make just emphasises the point that you are indeed he, and attempting to foist off this nonsense as if it weren't is intellectually dishonest. If you weren't he then why get bothered abuot the comments on its presentation?

Of course there could be two people who post on identical topics here, in identical fashoin, I suppose. And you might not be at all related to the Jose of that post on the arxiv. But twice now you've put a link to it, just raising suspicions once more.

 

[waht]

"In September 2006, Penny Smith of Lehigh University posted a paper on arXiv claiming to "prove the existence of a smooth solution for all time--under physicially reasonable hypothesis on the initial data--for the Navier-Stokes System in three dimensions."[1] On October 8, 2006, this paper was withdrawn by the author due a serious flaw."

From Wiki

http://en.wikipedia.org/wiki/Navier_Stokes


Interesting how this unfolds, Andrew Wiles also found a major flaw in his proof of FLT, but quickly corrected it. I mean if this error is too serious that undermines the whole proof.

 

[gocindygo]

Penny Smith's paper may have been withdrawn but this recent solution to the Navier-Stokes equations by David Purvance is still standing:

http://arxiv.org/abs/math.AP/0610086"

The Arbitrarily-Close and Convergent Fer Product Solution to the Three Spatial Dimension Navier-Stokes Equations.

 

[Gib Z]

If they really have found solutions then this shud be headline news lol, because these equations have been found to describe the motions in the universe, which is obviously surprising as these equations were orignally intended to describe fluid motion, correct me if I am wrong. And also, all of us here, talking as if we know anything about the Riemann hypothesis, like were all mathmaticians. seriously, i swear if ANYONE knows crap about it, its matt grime, and even he probably has troubles understanding the proof. I swear, we all think were smarter than we really are.

 

[neutrino]

And also, all of us here, talking as if we know anything about the Riemann hypothesis, like were all mathmaticians. seriously, i swear if ANYONE knows crap about it, its matt grime, and even he probably has troubles understanding the proof. I swear, we all think were smarter than we really are.

Like everyone knows what's really happening inside the White House, or Iraq, or N.Korea. This is just math gossip, and everyone who is anyone can gossip.

 

[matt grime]

I know very little about the Riemann Hypothesis (and since there isn't a proof of it, Gib I certainly can't understand that).

 

[J77]

Who was this Penny Smith?

And if you "solve" NS, are arxiv and a blog good places to get comments from?

 

[neutrino]

Who was this Penny Smith?

And if you "solve" NS, are arxiv and a blog good places to get comments from?

You might be interested in the article which came out last week...
http://www.seedmagazine.com/news/2006/10/the_proof_is_in_the_blogging.php

Incidentally, I came across the link in the aforementioned blog.

 

[quasar987]

Penny Smith is from what I've heard a ~40 year old doctoral student.

 

[neutrino]

Wow! She must be good then; especially with a Ph.D at age 12.

# Penelope Smith

* Associate Professor (on leave)
* Ph.D., Polytechnic Institute of Brooklyn, 1978.
* Differential geometry and geometric measure theory

http://www.lehigh.edu/~math/faculty.html

 

[J77]

You might be interested in the article which came out last week...

Thanks for the link - poor woman, seems the blog wasn't all her fault. Still it shows that you shouldn't be eager to post something, which you think corrct and which the whole world will look at, on arxiv!

 

[neutrino]

Still it shows that you shouldn't be eager to post something, which you think corrct and which the whole world will look at, on arxiv!

I never said/thought it was correct. See the '??' the title?

 

[shmoe]

Yeah, I called my local newspaper yesterday to see if they wanted to run a note mentioning this.

I'm a little late commenting, but this sort of thing is a bad idea. getting 'results' announced in the popular press before they are 'results' makes mathematicians look like tools to the general public if they have to be retracted. It's not a good idea to have the public thinking mathematicians can't even tell when they have solved a problem or not. Even loads of "alleged" or "supposed" or 'proposed" in front of the word "proof" in a newspaper article won't necessarily keep the publics views positive.

Still it shows that you shouldn't be eager to post something, which you think corrct and which the whole world will look at, on arxiv!

Why not? It makes the article more available to the relevant people, i.e. the experts capable of understanding the paper, compared to passing out copies to individuals (this won't make much of a difference if the pool of relevant experts is small enough). I mean you obviously expect the authors will make every effort to be sure their work is accurate, but mistakes do make it off peoples desks, and make it past colleagues they've communicated with privately, and past seminar rooms, etc. If it was someone who read her paper on arxiv that pointed out the flaw, then I'd say arxiv did it's job of getting it into the right hands.

 

[J77]

I never said/thought it was correct. See the '??' the title?

Not you!

The post made on arxiv.

 

[J77]

Why not? It makes the article more available to the relevant people, i.e. the experts capable of understanding the paper, compared to passing out copies to individuals (this won't make much of a difference if the pool of relevant experts is small enough). I mean you obviously expect the authors will make every effort to be sure their work is accurate, but mistakes do make it off peoples desks, and make it past colleagues they've communicated with privately, and past seminar rooms, etc. If it was someone who read her paper on arxiv that pointed out the flaw, then I'd say arxiv did it's job of getting it into the right hands.

You'd get much better feedback if you handed it out to individual people that you know are good in the field and that you know will give good criticism.

'Experts' don't have the time to take papers of arxiv and check for their accuracy - particularly w.r.t. a problem like this.

And I'm sure the mistakes on a topic of this size would be picked up by the journal referees.

 

[shmoe]

You'd get much better feedback if you handed it out to individual people that you know are good in the field and that you know will give good criticism.

Of course you want it in the hands of the experts you know, arxiv isn't stopping that. It can make it available to both the experts you want and others.

'Experts' don't have the time to take papers of arxiv and check for their accuracy - particularly w.r.t. a problem like this.

Was her error found by someone who read the paper on arxiv? I don't know.

experts certainly had the time to read perelman's work on arxiv. What do you think about the approach he took?

And I'm sure the mistakes on a topic of this size would be picked up by the journal referees.

I'm not. Referees are not guaranteed to pick up all the errors. There's a reason that the clay prize requires your work to stand for a year before being accepted, after it's published it will face the scrutiny of everyone interested, not just a few referees.


To be more clear, I'm not saying arxiv should be a dumping ground for things people "kinda, maybe" think are correct. I don't think it's wrong to use it to quickly spread work that you're 'pretty darn confidant' is correct, provided your version of 'pretty darn confident' is not in general wasting peoples time. Maybe it is wrong, I dunno. Maybe it should just be used to make pre-prints of articles already accepted for publication available.