# Another Millenium Problem May Have Been Solved

#### Zonk posted more than 7 years ago | from the we-all-miss-our-loved-ones-and-gas-equations dept.

134
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."*

## Tyler Hoyt BABY (1)

## riff420 (810435) | more than 7 years ago | (#16345893)

## Pretty nifty stuff (1)

## Morlark (814687) | more than 7 years ago | (#16345901)

## Hm. (5, Funny)

## ZombieRoboNinja (905329) | more than 7 years ago | (#16345905)

LOUD ones.

## Re:Hm. (0)

## Anonymous Coward | more than 7 years ago | (#16345921)

## Re:Hm. (5, Funny)

## arun_s (877518) | more than 7 years ago | (#16346159)

## Re:Hm. (1)

## plantman-the-womb-st (776722) | more than 7 years ago | (#16346525)

You sir have pwned me.

## pr0n (2, Funny)

## macadamia_harold (947445) | more than 7 years ago | (#16345943)

This new solution is for Navier-Stokes equations under physically reasonable conditions. Navier-Stocks equations describe the motion of fluid substances such as liquidswho needs a description of the motion of fluid substances? I want video, perferably in slow-motion and from multiple angles.

## Re:pr0n (1)

## Ignominious Cow Herd (540061) | more than 7 years ago | (#16348307)

## Smoother rendition possible... (2, Funny)

## nixkuroi (569546) | more than 7 years ago | (#16345945)

Don't player hate, player appreciate baby.

## Re:Smoother rendition possible... (1)

## Prune (557140) | more than 7 years ago | (#16346945)

## Re:Smoother rendition possible... (0)

## Anonymous Coward | more than 7 years ago | (#16347827)

## Re:Smoother rendition possible... (1)

## bodan (619290) | more than 7 years ago | (#16348001)

## Re:Smoother rendition possible... (-1, Offtopic)

## Anonymous Coward | more than 7 years ago | (#16350489)

What makes you think that? There have been some scams (snake oil and the like) but energy healing is real.

Try this: when you pray (if you're religious/spiritual; it's not necessary because all humans can do this, so if you're not religious you can just press your palms together and not pray), breathe deeply. Fill your lungs, until your shoulders rise, then empty them completely. Use your diaphragm as well to maximize the air exchanged with the environment. You don't have to breathe fast (although that does help), you just need to breathe deeply.

For me, it took 30-40 hours of practice before I began "feeling the energy". To me, it feels like a tingling, similar to the feeling when a body part "falls asleep" -- except it's a light tingling and I can still feel sensations in my hands, they're not numb.

It's okay to mod me down, because I'm not saying something that is unverifiable. I realize that 30-40 hours is a bit of effort to verify, but I did it and was very skeptical that it would work, even while doing it; it still worked, and now I don't need to believe -- I

know, I have experienced it.We do not yet have equipment sensitive enough to measure this "energy". That doesn't mean it doesn't exist, or that the sensations I feel are not real (or that the healing I've experienced in my weak joints was somehow faked). In the past, we did not yet have equipment sensitive enough to measure bacteria and viruses, but people still died by the thousands of various plagues. (I.e., "Absence of evidence is not evidence of absence.")

I am sorry that you had a bad experience. I'm not here to sell anything. It worked for me, and I'm positive it will work for you if you attempt it, even with a closed mind (like mine was). Just breathe deep; that's the only requirement, and it

isa requirement. Once you've felt it, you can achieve it with less breathing, but the breathing is necessary; it's something in the air.The specific technique that I learned was Jin Shin Jyutsu. The book "The Touch of Healing" is how I got started. I've also read "Quantum Touch". You don't need to buy these, they should be available through your local library (or via inter-library loan). Good health!

## Neat indeed (3, Interesting)

## Zx-man (759966) | more than 7 years ago | (#16345993)

Note: Not considering

P vs. NPas it is quite possibly unprovable.## Re:Neat indeed (1)

## ZorbaTHut (126196) | more than 7 years ago | (#16347041)

It certainly couldn't ever be proven unprovable, like some things can be, since proving it unprovable would also prove there was no way to implement a conversion P = NP, and, therefore, P != NP.

Just because we can't prove it doesn't mean it's unprovable.

## Re:Neat indeed (2, Informative)

## Famatra (669740) | more than 7 years ago | (#16347559)

How could it be unprovable?

Just because we can't prove it doesn't mean it's unprovable.

Godel's incompleteness theorems [wikipedia.org]

## Re:Neat indeed (2, Interesting)

## ZorbaTHut (126196) | more than 7 years ago | (#16347923)

## Re:Neat indeed (4, Insightful)

## Garse Janacek (554329) | more than 7 years ago | (#16348287)

Not necessarily -- it is conceivable that there exists a poly-time algorithm for an NP-complete problem,

butthere is no proof (within ZFC, say) that it is correct. The physical truth is certain -- but what we canknowabout 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:Neat indeed (0)

## Anonymous Coward | more than 7 years ago | (#16348909)

## Re:Neat indeed (1)

## AxelBoldt (1490) | more than 7 years ago | (#16350235)

## Re:Neat indeed (1)

## rbarreira (836272) | more than 7 years ago | (#16347771)

## Re:Neat indeed (1)

## ZorbaTHut (126196) | more than 7 years ago | (#16347885)

So even if it does turn out to be independent of current accepted axioms, which I will admit I'm skeptical about, I feel that knowing that allows us to immediately add an axiom to make that view of math approach "physical computer hardware". Or, alternatively, to define a subset of all NP problems that include things like Hamiltonian path.

## Re:Neat indeed (1)

## AxelBoldt (1490) | more than 7 years ago | (#16350281)

## Re:Neat indeed (1)

## jonadab (583620) | more than 7 years ago | (#16347761)

This Navier-Stokes thing seems to be more of an applied-math problem, and although I'm sure it's important, it's just not as exciting to me as the more abstract theoretical stuff of pure math.

## Re:Neat indeed (1)

## rogerdr (745180) | more than 7 years ago | (#16348761)

## Re:Neat indeed (1)

## be-fan (61476) | more than 7 years ago | (#16349915)

## Re:Neat indeed (2, Informative)

## AxelBoldt (1490) | more than 7 years ago | (#16350339)

must exist, without saying what it looks like or how to get it. It's of pure intellectual interest and won't help the engineers in any immediate way.## Re:Neat indeed (-1, Troll)

## Anonymous Coward | more than 7 years ago | (#16347997)

## Ouch... (-1, Offtopic)

## Anonymous Coward | more than 7 years ago | (#16346013)

Someone needs to get laid. Any volunteers? Take one for the geek team, she's lonely!

Am I right, or am I right? I'm right.

## Re:Ouch... (1, Funny)

## tsq (768711) | more than 7 years ago | (#16346075)

## Re:Ouch... (1, Funny)

## richy freeway (623503) | more than 7 years ago | (#16346131)

## Re:Ouch... (0)

## Anonymous Coward | more than 7 years ago | (#16348271)

## Quite impressive (5, Informative)

## adityamalik (997063) | more than 7 years ago | (#16346037)

## Re:Quite impressive (5, Informative)

## S3D (745318) | more than 7 years ago | (#16346187)

## Re:Quite impressive (5, Informative)

## vogon jeltz (257131) | more than 7 years ago | (#16346563)

it's about the existence of a solution for certain boundary / initial conditions of the NSEs. This is still a very big deal because you can now expect correct results when doing numerical calculations. By the way you probably meant FEM (Finite Element Method), not "fractional element methods". FEM is rarely, if not at all used for solving the NSEs, you'd rather use Finite Volume Methods (applicable for structured and unstructured grids, as are FEM).

## FEM is used plenty for solving Navier-Stokes (1)

## Richard Mills (17522) | more than 7 years ago | (#16350779)

The choice of method for solving the equations

doesseem to vary quite a bit between disciplines. Engineers tend to love FEM, while, say, atmospheric modelers seem to prefer finite-volume or finite-difference approaches.## Re:Quite impressive (0, Offtopic)

## OmnipotentEntity (702752) | more than 7 years ago | (#16347399)

Here's an example. Two board, one 3m and one 2m are laying crisscross in an alley, with one end in each corner of the alley, and laying the other end on the opposite wall.

Their intersection is exactly 1m from the ground, how wide is the alley?

This problem is very easy to find a numeric solution, but suprisingly difficult to find the exact solution [nerdparadise.com] (by hand). But we already know the method to find it, it's simple algebra.

Just because an exact solution exists doesn't mean it's pratical or it will be used, if the approximation is good enough, or much faster. As I understand it though, Fluid Dynamics is a chaotic system. So an exact solution is probably preferrable unless the calculation disparity is wide enough. Just thought I'd point out the obvious because no one else was doing it.

## Re:Quite impressive (1)

## This is outrageous! (745631) | more than 7 years ago | (#16348291)

You take a quartic equation [nerdparadise.com] and choose to call "exact" what is called "a solution by radicals".

Yes, a solution by radicals can be hard to find even when it turns out to exist. (Indeed quartics weren't solved by radicals until Ferrari in 1540.)

But the question whether a solution by radicals exists has nothing to do with whether a solution (period) exists. Indeed polynomial of higher degree have the latter (Gauss' fundamental theorem of algebra) but not always the former (Abel's quintic counterexample).

Penny Smith's achievement is analogous to Gauss's and not *at all* to Ferrari's.

Fortunately the former, not the latter, is what's needed to guarantee that numerical methods (e.g. Newton's, in the analogy) converge to an actual solution rather than nonsense.

## Re:Quite impressive (3, Funny)

## pipingguy (566974) | more than 7 years ago | (#16346471)

## Re:Quite impressive (0)

## Anonymous Coward | more than 7 years ago | (#16346715)

## A series of tubes? (1)

## tepples (727027) | more than 7 years ago | (#16347833)

You mean the series of tubes that make up the Internet?

## Re:A series of tubes? (1)

## pipingguy (566974) | more than 7 years ago | (#16349469)

## Re:Quite impressive (3, Funny)

## legrimpeur (594896) | more than 7 years ago | (#16346639)

but rather the PROOF of THE EXISTENCE OF A FORMAL SOLUTION. You still have to find it,

either analytically or (most probably) numerically.

Bottom line: about this a mathematician gets horny, an engineer says SO WHAT!!!

Ciao

## Re:Quite impressive (1)

## WhoBeDaPlaya (984958) | more than 7 years ago | (#16347597)

## Re:Quite impressive (1)

## pyite (140350) | more than 7 years ago | (#16349305)

existenceof solutions. At times, we even care about theuniquenessof such solutions. Or, how about convergence of the series we're approximating a function with? Or maybe, does this Fourier series really work on this set of data that has a bunch of discontinuities in it?Here is [umn.edu] what happens when such problems aren't approached with proper rigor. In short, we read (regarding an offshore oil drilling platform):

The post accident investigation traced the error to inaccurate finite element approximation of the linear elastic model of the tricell (using the popular finite element program NASTRAN). The shear stresses were underestimated by 47%, leading to insufficient design. In particular, certain concrete walls were not thick enough. More careful finite element analysis, made after the accident, predicted that failure would occur with this design at a depth of 62m, which matches well with the actual occurrence at 65m.So, yes, engineers VERY MUCH care about these things.

## You know what's more impressive? (0)

## Anonymous Coward | more than 7 years ago | (#16348133)

## As long as we get ... (0)

## Anonymous Coward | more than 7 years ago | (#16351549)

## Whuh? (5, Funny)

## LiquidEdge (774076) | more than 7 years ago | (#16346063)

## meh (0)

## Anonymous Coward | more than 7 years ago | (#16346311)

## Why the constant Slashdot self-hate? +5 funny (1)

## SaberTaylor (150915) | more than 7 years ago | (#16348935)

## Stop killing the Amish (-1, Offtopic)

## Anonymous Coward | more than 7 years ago | (#16346079)

It is a just act in the eyes of the Lord only to kill Jews, homosexuals, and Islamists. Amish persons and other Prostestants are off limits. I hope this clears things up.

## Someone had better tell the Formula One teams (3, Interesting)

## Simulacrus (1003107) | more than 7 years ago | (#16346111)

## Re:Someone had better tell the Formula One teams (3, Informative)

## Overzeetop (214511) | more than 7 years ago | (#16346839)

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

## quanminoan (812306) | more than 7 years ago | (#16348389)

verygood 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.## I solve 3 millennium problems before breakfast (3, Insightful)

## fatphil (181876) | more than 7 years ago | (#16346137)

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

## Ah, one of those math stories (-1, Troll)

## Anonymous Coward | more than 7 years ago | (#16346157)

## Spell check (0, Offtopic)

## MrYotsuya (27522) | more than 7 years ago | (#16346173)

## A LIFE ON THE TOILET: THE SCOTT LOCKWOOD STORY (-1, Offtopic)

## Anonymous Coward | more than 7 years ago | (#16346211)

## blink blink ! (1)

## phreakv6 (760152) | more than 7 years ago | (#16346279)

## Re:blink blink ! (0)

## Anonymous Coward | more than 7 years ago | (#16346371)

## Re:blink blink ! (0)

## Anonymous Coward | more than 7 years ago | (#16346635)

## Re:blink blink ! (2, Interesting)

## the eric conspiracy (20178) | more than 7 years ago | (#16347503)

One of the things that I understood was a real problem with NS is that not only were there no existence proofs, but there were no uniqueness proofs. Does nayone know if the uniqueness question has been answered?

## It's the mathematics of .... (0, Offtopic)

## PermanentMarker (916408) | more than 7 years ago | (#16346295)

hahahaha

oops (sorry)

## Re:It's the mathematics of .... (2, Interesting)

## thomasa (17495) | more than 7 years ago | (#16346887)

http://en.wikipedia.org/wiki/Catastrophe_theory [wikipedia.org]

## 'kinell. (0)

## Anonymous Coward | more than 7 years ago | (#16346339)

It's "millennium".

## Millenium? (1)

## Threni (635302) | more than 7 years ago | (#16346381)

## Re:Millenium? (1)

## eric.t.f.bat (102290) | more than 7 years ago | (#16347595)

## I am not amused. (1)

## Millennium (2451) | more than 7 years ago | (#16348359)

landnboth appear twice. But then, this is Slashdot; correct spelling may not be a reasonable expectation.## Cancel the survival gear! (1)

## AndroidCat (229562) | more than 7 years ago | (#16349505)

## The toughest millenium problem of all... (3, Funny)

## john-da-luthrun (876866) | more than 7 years ago | (#16346477)

thatone would be a million dollars ofanybody'smoney...## Re:The toughest millenium problem of all... (4, Funny)

## Frater 219 (1455) | more than 7 years ago | (#16350207)

A mille

nnium ismille + annus: a thousand years.A mille

nium ismille + anus: a thousand assholes.If you get it wrong, you're anal; if you get it right, you're annual.

## The toughest mathematical and computational probs (1)

## Sem_D_D (175107) | more than 7 years ago | (#16346701)

I suspect, some fancy hardware and breakthrough programming was needed to assist the geniuses, that managed to pull this one out.

That is a good sign of the advances in this outer-limits areas.

## What is the geometry? (2, Informative)

## 140Mandak262Jamuna (970587) | more than 7 years ago | (#16346747)

Abstract of this postIt is a big deal for the mathematicians. That is allThe N-S Eqn has been "solved" in 2D using Velocity Potential, Stream Function approach. But in 3D stream function does not exist and the method does not extend. But in practice the only problem that is really "solved" even in 2D was was this driven cavity problem, a box with a moving wall.

Take the much more simple to solve for a hundred years, the Heat Equation. Analytical solutions exist for simple domains like a semi infinite plate or a box with Dirichlet boundaries. But in practice ANSYS sells numerical solutions to Heat Equations and the industry has been buying millions dollars worth every year. Similarly FLUENT (Recently acquired by ANSYS) does not have to worry its market has fallen out of the bottom. For real life geometries we will be using numerical solutions of NS Eqn for the foreseeable future.

Further though I could not see any geometry restrictions in the paper, it appears as though they have just proved solutions exist, and not actually solved it. Depending on the assumptions made and terms neglected, engineers may be able to build better turbulence ing out of this.

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.

## Re:What is the geometry? (1, Insightful)

## Anonymous Coward | more than 7 years ago | (#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:What is the geometry? (2)

## Hakubi_Washu (594267) | more than 7 years ago | (#16346883)

It is a big deal for the mathematicians. That is allI wouldn't go so far as to say it is only interesting for mathematicians. Fluid dynamics and Navier-Stokes especially, is what, for example, many 3D engines use to simulate water by now. Granted, they use simplified equations, usually only taking the surface into consideration, but any breakthrough in the theory their models are based on might have implications for those models as well. I'd say let's wait until a) those new findings have been properly peer-reviewed and b) more computer scientists, engineers, and other theory-appliers have had a few months of thinking about it.

## An important step (5, Informative)

## Orp (6583) | more than 7 years ago | (#16346919)

Back to the paper... While I am not a mathematician, the paper appears kind of rough to me - lots of punctuation errors, commas in the wrong place, unclosed parehtneses... I suspect this paper has not been fully through the peer review process. I don't know how the mathematicians do it, but I would say this paper is a draft (not discrediting the work - I am not quallfied to judge it - but it looks rough).

## Re:An important step (2, Informative)

## Anonymous Coward | more than 7 years ago | (#16347921)

I suspect this paper has not been fully through the peer review process. I don't know how the mathematicians do it, but I would say this paper is a draft (not discrediting the work - I am not quallfied to judge it - but it looks rough).Not that I think you are making an attack on mathematicians here, but I just want to comment on this for anyone that might construe it as such.

Mathematicians do subject papers to full peer review before being published in any reputable journal, but the arXiv is not a journal in any sense of the word. It's a sever that holds preprints --- literally ANYONE can put ANY paper on it. There are dozens of papers there that claim to have solved the Goldbach conjecture, or the Riemann hypothesis, or proven that the real numbers are countable, etc.

Likely this paper has not been peer reviewed at all. Take it with a pound of salt.

## Re:An important step (2)

## jschrod (172610) | more than 7 years ago | (#16348089)

## Re:An important step (1)

## Ibag (101144) | more than 7 years ago | (#16349083)

## Re:An important step (1)

## egork (449605) | more than 7 years ago | (#16351737)

Proof: This is less than proved in the brilliant paper of [H]. QED.## a fitting tribute (1)

## seven of five (578993) | more than 7 years ago | (#16347319)

## Going to need to follow how this reviews (1)

## StressGuy (472374) | more than 7 years ago | (#16347343)

## What the World Needs (1)

## Baby Duck (176251) | more than 7 years ago | (#16347433)

## yeah, right (0)

## Anonymous Coward | more than 7 years ago | (#16347565)

"Immortal" ?

"three space dimensions"?

Now, if the title was "Time-invariant solution of the Navier-Stokes equation in three dimensions", okay.

But the choice of words for the title indicates kook-infestation.

## Re:yeah, right (1)

## AxelBoldt (1490) | more than 7 years ago | (#16350445)

## Shitd?! (-1, Redundant)

## Anonymous Coward | more than 7 years ago | (#16347683)

## Engineer here.. and can I say WOW! (1)

## PWNT (985141) | more than 7 years ago | (#16347939)

## An arxiv article does not a headline make (2, Interesting)

## Wooster_UK (963894) | more than 7 years ago | (#16347973)

As I say, far be it from me to call "crank", but I'd wait for this to appear in a peer-reviewed journal

andget responses. I suspect the Millennium (sp!) Prize committee may well be doing likewise.## Re:An arxiv article does not a headline make (2, Informative)

## flawedconceptions (1000049) | more than 7 years ago | (#16348099)

## Re:An arxiv article does not a headline make (1)

## Wooster_UK (963894) | more than 7 years ago | (#16348547)

## Shoehorning in my field (1)

## mnemonic_ (164550) | more than 7 years ago | (#16348035)

## Re:Shoehorning in my field (1)

## Krakhan (784021) | more than 7 years ago | (#16349763)

## What millennium? (0)

## Anonymous Coward | more than 7 years ago | (#16348371)

## Last claim of sexists falls (-1, Offtopic)

## joneshenry (9497) | more than 7 years ago | (#16348447)

Christina Sormani has a web page [cuny.edu] explaining why Penny Smith is likely to have solved the Millenium Problem on the Navier-Stokes equation. Smith's paper is the culmination of a lifetime of research similar to how Wiles' proof of Fermat's Last Theorem was a logical outcome of his previous research. This is not someone coming from out of nowhere providing a proof that has nothing to do with his or her prior specialty.

The debate is now over. Penny Smith has shown that there is in fact no variance between men and women that predisposes men to have the very top mathematicians. In fact the proof that environment trumps genetics has been demonstrated in the United States over the past decades: males born in the United States have been judged by government and industry to not be good enough in top-level mathematics which is why so much talent has to be imported from other countries. The United States is probably going to follow the path of the United Kingdom where cultural factors are causing boys mathematical achievement in school to collapse [guardian.co.uk] relative to that of girls.

## Re:Last claim of sexists falls (0)

## Anonymous Coward | more than 7 years ago | (#16348651)

The example of Penny Smith, I'm afraid, cannot by itself disprove the general statistical assertion of greater variance for males. For that, one needs large scale group studies.

## Re:Last claim of sexists falls (0)

## Anonymous Coward | more than 7 years ago | (#16349823)

Let's send Penny down to Miami, and have her tweak the NHC's computer modelling programs,

so that we'll know exactly where the next hurricane will strike and with what wind speeds

and rainfall rates, etc.

Either that, or have her clone herself, and work the problem in parallel, and then teach

scads of other young minds how to do it.

## Re:Last claim of sexists falls (0)

## Anonymous Coward | more than 7 years ago | (#16349835)

So there is all that bullshit talk about being men better than women because they tend to have a greater variance (hence having the best and worst results) and you just now disproved it because this one women solved a Millennium Prize?

Poor Marie Sklodowska Curie (who won two Nobel Prizes and was one of the few people to do it)... why didn't you use her for you counter-example? At least her work is already proved, unlike the work from this lady.

Statistical significance comes from the size of the studied population. Otherwise, based on this:

"A B-17 ball turret gunner, Magee had no choice but to jump out of a disabled, spinning-out-of-control bomber from about 22,000 feet.

A drop of more than four miles. Without a parachute. And Magee miraculously lived." (taken from here [209.157.64.200] )

jumping of a comercial airplane in trouble would be less risky than waiting for it to try to emergency land (as we know people die on plane crashes and apparently free-falling people do not).

So, next time will you jump of the airplane? Thought so...

## another explanation (1)

## David Eppstein (306415) | more than 7 years ago | (#16349337)

## ...Waitaminute. (0)

## Anonymous Coward | more than 7 years ago | (#16349797)

## Penny Smith's usenet posts! (2)

## programmeratarms (704583) | more than 7 years ago | (#16350385)