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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."

cancel ×

134 comments

Tyler Hoyt BABY (1)

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

WHAT WHAT

Pretty nifty stuff (1)

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

If this turns out to be true, then it's a pretty big deal. I remember studying this kinda stuff a few years ago... suffice to say that it really makes my head hurt, even now. Having had a quick look at the article, it does promise to be a very interesting read, at the very least.

Hm. (5, Funny)

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

I have no idea what any of that means, but rest assured that by the time this thread ends I will have developed ironclad opinions on the subject.

LOUD ones.

Re:Hm. (0)

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

You sir, are my hero. . .

Re:Hm. (5, Funny)

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

I have a truly remarkable proof that will convince you, but the dang lameness filter is getting in the way.

Re:Hm. (1)

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

Never before have I laughed this hard at a slash post.

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 liquids

who 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)

I believe you are thinking of a different Stokes [suzannestokes.com] .

Smoother rendition possible... (2, Funny)

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

I bet if I put on a pimp hat and read it while drinking a glass of Courvoisier, I could make it "The Even Smoother Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System".

Don't player hate, player appreciate baby.

Re:Smoother rendition possible... (1)

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

Courvoisier is anything but smooth. Try a proper cognac like Delamain or Hennessy (assuming X.O or older of each brand, of course).

Re:Smoother rendition possible... (0)

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

Whoooosh!

Re:Smoother rendition possible... (1)

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

sqr("Woooosh!");

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

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

"Alternative/natural medicine: BIGGEST. SCAM. EVER." --I

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 is a 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)

As a math major I may say the this is impressive: after understanding the significance and complexity of the problem seeing a solution has been found is really exciting. Although I'm looking forward to see something done about the most significant of the Millennium Problems (IMO and from the pure maths POV) -- the Riemann hypothesis [wikipedia.org] .

Note: Not considering P vs. NP as it is quite possibly unprovable.

Re:Neat indeed (1)

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

How could it be unprovable?

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)

That is true. However, note that unlike Godel's incompleteness theorem, P = NP has direct and obvious connections to the real world. We're not choosing between competing logical theories that exist in a vacuum. P = NP allows us to do certain interesting things on computers. If it turns out we can prove we'll never be able to do those, that is the same thing as saying it is impossible.

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, 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:Neat indeed (0)

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

And why NOT tack on another axiom (like the axiom of choice)? Having trouble with your proofs? Make up a corny axiom that magically "solves" them for you, reality be damned! ZFCX, where X is the Axiom of "Damn My Dissertation Needs Some Help."

Re:Neat indeed (1)

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

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.
Yes, that's conceivable but seems unlikely. A more likely scenario (and in fact my money is on it) is that we can eventually prove that ZFC can neither prove nor disprove P=NP, and in that case we don't know whether your scenario above is correct, or if on the contrary no such algorithm exists but ZFC is simply too weak to establish that.

Re:Neat indeed (1)

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

It can be independent of the current accepted axioms.

Re:Neat indeed (1)

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

That's true. However, P = NP is interesting because it has practical uses. So, while there is obviously a mathematical meaning to it, the part that I am personally interested in is "is it doable on modern computer hardware".

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)

"is it doable on modern computer hardware"
The question P=NP is thoroughly uninteresting when restricted to existing computers. Every existing computer has a finite and bounded amount of memory and storage, and hence a finite set of internal states, and is therefore a finite state machine. Everything a finite state machine does can be done in linear time.

Re:Neat indeed (1)

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

Indeed. When it became evident that the Poincaire conjecture is not going to be considered an open problem much longer, my thoughts too were of the Reimann Hypothesis. Throughout most of the twentieth century those were widely considered to be the two biggest open problems in pure math, and it'd be really cool to see them both solved in our generation.

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)

I'd say that this can be considered a 4D generalization of complex analysis, if true. In that case, it could go far beyond applied math into Relativity.

Re:Neat indeed (1)

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

See, from my POV (I'm an engineer), an analytic solution to Navier-Stokes would be far more important. It would mea a huge advance for our understanding of aerodynamics (among other fluid-flow problems).

Re:Neat indeed (2, Informative)

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

This Navier-Stokes thing seems to be more of an applied-math problem
Not really. Actually solving Navier-Stokes for concretely given boundary conditions is very much an applied math problem, maybe the most important one of them all, and it is done with computers and algorithms from numerical analysis. But the paper we're discussing here is pure math: she proves that for a certain class of boundary conditions a solution 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)

I wonder if your post would have been modded up at all had you not said "As a math major." Shut the fuck up, no one cares.

Ouch... (-1, Offtopic)

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

She wrote a paper entitled "A regularity result for singular nonlinear elliptic systems in inverse-power weighted Sobolev spaces."

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)

Female AND good at math? What else could a /.er ask for?

Re:Ouch... (1, Funny)

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

A free lifetime WoW subscription?

Re:Ouch... (0)

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

Your ridiculous anti-intellectualism is a disgrace to geekdom.

Quite impressive (5, Informative)

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

As a mechanical engineer, I have some idea of what this means.. Fluid dynamics is a fairly pervasive subject which goes into the design of airplanes, irrigation canals, industrial machinery, turbines and a lot of other places. The solution of the navier stokes' equation in three dimensions is quite fabulous, since without such a mathematical tool it's not possible to estimate how a fluid will flow in three dimensions.. Till now, we typically use either special conditions (ex. along a turbine blade, constant pressure) or fractional element methods (think of fluid as lots of tiny balls) or physical modelling for such problems. To put some perspective, it's about as cool as being able to determine the movement of n planets simultaneously attracting each other gravitationally.. quite tough!

Re:Quite impressive (5, Informative)

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

That is not "the solution" of the Navier-Stocks system - they could be solved only numerically (fractional element methods or other discretization), but this is the next best thing - proof of the existance of such solution. From the practical point of view that mean, if you have correct physical starting conditions and working numerical method you will get correct result after calculation. Until now, you couldn't have been sure if you will get physyically reasonable result of numerical calculations, even if starting conditions would be correct.

Re:Quite impressive (5, Informative)

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

Correct,
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)

Why do you think that FEM is rarely used to solve the Navier-Stokes equations? A quick Google search will indicate otherwise.

The choice of method for solving the equations does seem 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)

IANA Expert in Fluid Dynamics; however, though an exact solution exists, this doesn't mean that it'll be easy to find even if we have a method or formula to solve it exactly.

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)

Your analogy is completely misleading.

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)

I agree. Fluid dynamics is very fascinating. Since I'm not so smart I've devoted my limited abilities to trying to understand the things we put conventional fluids into so that we can transmit them.

Re:Quite impressive (0)

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

You're a milkman?

A series of tubes? (1)

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

Since I'm not so smart I've devoted my limited abilities to trying to understand the things we put conventional fluids into so that we can transmit them.

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)

Information is a fluid now? You kids today with all your newfangled inventions...

Re:Quite impressive (3, Funny)

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

Actually the whole thing IS NOT about FINDING SOLUTION of the Navier-Stokes equations,
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)

It's kinda like trying to find an exact analytical solution for something as innocuous as the current distribution on a current carrying conductor for more accurate impedance calculations. Major PITA.

Re:Quite impressive (1)

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

Actually, engineers care about this a lot. Inexperienced people take a formula and assume it works under all conditions. However, when you take a [good] numerical analysis course, you'll do more than just learn how to use a formula. You'll spend time doing a lot of real analysis that you don't necessarily enjoy doing (I didn't) but the point is clear. A lot of times we really, really, care about existence of solutions. At times, we even care about the uniqueness of 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)

Your stupidity.

As long as we get ... (0)

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

quiet & more powerful leaf blowers

Whuh? (5, Funny)

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

Man, I haven't had a date in like 4 years, and even *I'm* not nerdy enough to know why this matters...

meh (0)

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

I have had a date in like.... ever and I don't understand this... ok.. ok at this point I must Concede that I am more a loser and less of a nerd... but still...

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

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

Did I miss the big event when nerdism became negative instead of positive?

Stop killing the Amish (-1, Offtopic)

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

Hello group, Benedict XVI, the Nazi Pope here. It has come to my attention that one of you recently shot up a schoolroom full of Amish children. Be advised that this is against the will of God and the Saviour.

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)

While I know they perform many, many computer simulations, I think aerodynamics is still regarded as one of the "black arts" in the field. Wind tunnels are still used extensively (it's often about who can build the better wind tunnel, never mind car). Maybe complete solutions of fluid movement will mean some odd-looking cars in 2007!

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

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

Not really. This proof of the existance of the solution won't substatially affect the real-world application of fluid dynamics (including aerodynamics) for quite a ling time (maybe within my lifetime, probably not). Numerical and real simulation will still guide the principal advances at the full assembly level. Nonetheless, this is a pretty cool event. I remember studying N-S in undergrad. Still makes the hair on the backof my neck stand up is apprehension. (tensor math and pdes both make me ill).

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

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

I solve 3 millennium problems before breakfast (3, Insightful)

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

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

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

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

Another one of those math stories where it's discussed entirely in the gibberish context it's initially presented in, while a good hundred or so posters talk as if they pretend to know what this material is about so they can look smart and whore karma points.

Spell check (0, Offtopic)

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

I wish that there were spell checks on whatever is submitted. "Millenium" indeed.

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

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

learn how one man can restructure his entire life to revolve around feces and farting. how one man has basically made defecation his career. yeah it's sick. but it's true, it's william scott lockwood and he is taking dumps on local toddlers, ugh, just horrible!!!! usa kicked him out to us here in whitehorse and let me say, yukon territory says go back to the states vlad you son of a bitch!!!!!!

blink blink ! (1)

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

the article could have very well been in french or latin

Re:blink blink ! (0)

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

I know french and some latin. I can say with confidence that it is neither language and I didn't understand anything either...

Re:blink blink ! (0)

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

It's all Greek to me.

Re:blink blink ! (2, Interesting)

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

I know some French, some Latin, and more math than either and have used the NS equation in my work (including nuerical slutions to subsets of the 3D problem). However ths would take me at least a couple of years of work to understand.

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)

it's about the mathematics of farting
hahahaha


oops (sorry)

'kinell. (0)

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

At least spellcheck the ARTICLE TITLES.

It's "millennium".

Millenium? (1)

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

I thought it was "Millennium"? Certainly that's how the linked-to website spells it.

Re:Millenium? (1)

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

Hey, go easy on them. They've only had seven years to learn how to spell the word. Don't rush them! I mean, look how long it took them to get a CSS-based layout for this site, and CSS is only three letters!

I am not amused. (1)

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

You are correct: the letters l and n both 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)

I was disappointed when there was no mention of a new Y2K-type problem.

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

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

...is getting people to spell it "millennium". Cracking that one would be a million dollars of anybody's money...

Re:The toughest millenium problem of all... (4, Funny)

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

Just remember:

A millennium is mille + annus: a thousand years.
A millenium is mille + 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)

The fliud dynamics is an area, which is purported to be on the current edge of supercomputer capabilities, along with nuclear weapons simulation, weather forecasting and GO http://en.wikipedia.org/wiki/Go_board_game/ [wikipedia.org] . Chess, on the other hand, is no longer part of this exclusive club, as the comparison says http://en.wikipedia.org/wiki/Go_board_game#Numeric al_estimates [wikipedia.org] .
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 post

It is a big deal for the mathematicians. That is all

The 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 all

I 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)

As a previous commenter stated, this is a mathematical proof that such a solution exists. You cannot explicitly solve the Navier Stokes equations as written. If you could, my job would be much easier (I model thunderstorms at very high resolution on massively parallel supercomputers). The Navier Stokes equations, along with some other conservation laws, and some physical parameterizations, can be "closed" such that you can approximate a solution using numerical tehcniques, given an initial state and boundary conditions. It is not easy. From a practical standpoint, dealing with massively parallel computers is not much fun. I've spent the past couple of months debugging my own stupid coding errors, competing with hundreds of other scientists running their models, and finding ways to manage the terabytes of data these models produce when they do run succesfully.

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)

[On arXiv,] 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.
The difference is that the authors of these papers have no track record of getting articles accepted in the best math journals, also have no track record of previous ground breaking new work in math, and have not caused a stir in the community that is as positive as it is this time. Penny Smith has.

Re:An important step (1)

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

The arXiv (pronounced "archive") is a preprint server where people post their papers. Sometimes the papers are awaiting publication, sometimes they aren't going to be published, and sometimes they are just rough things like lecture notes that people just figure others might appreciate. As such, it is fairly unsurprising that the paper would be a rough draft. That doesn't mean that the ideas aren't all there, but it most likely hasn't been peer reviewed in any broad sense yet. Putting it on the arXiv is perhaps a first step in getting peers to look it over.

Re:An important step (1)

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

I wonder, if what they wanted to say was "this is more then proved"?
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)

it's about time someone named an institute after Clay Aiken [google.com]

Going to need to follow how this reviews (1)

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

A generic solution of Navier-Stokes under any kind of realistic conditions is huge. I'm sure it will still be necessary to discretize for most aircraft or boats. I'm also certain the solution is "strange" (as in "highly sensitive to boundary conditions") in many cases. Still, this is a major breakthrough if it verifies.

What the World Needs (1)

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

I'm holding out for a solution to the Navel-Strokes system.

yeah, right (0)

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

Sorry, but this doesn't pass the sniff test, just on the basis of the title.

"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)

You're wrong. "Immortal" in this context is standard terminology for a solution that exists for all times. Your choice of "time-invariant" is not the same. "Three space dimensions" is much clearer than your "three dimensions", because the latter could be mistaken for one time and two space dimensions, a much simpler scenario.

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

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

not that WOW, but the surprise! If there do exist solutions to the navier-stokes equations be prepared for something huge. These equations play a dominating role in anything where something is moving in the presence of many other moving particles (think water, gas, landslides etc) The significance of this finding cannot be emphasized enough, if it proves to be true. Current solutions revolve around using computers to actually simulate the ENTIRE section of the system you want, then you test for conditions at specific points. Also, only sufficiently large systems will give an answer, as you try to get a finer and finer solution to a zoomed in region, the data and simulation available either gets too small to work with, or you get so many non-linear equations to simultaneously solve that it takes up too much RAM and memory. Second: The existance of a solution to these groups of NON-LINEAR equations may provide an answer to how non-linear equations react to starting conditions. I am personally very excited about this, and hope it pans out properly.

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

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

Hmmm... the arxiv, of course, has a bit of a 'reputation'. They'll take anything, and more power to them for being willing to do so. However, it does tend to mean that if one's a non-specialist, the cranks can look awfully convincing. Without, obviously, wishing to ascribe that appellation to the good Associate Professor, I would note that this paper carries some of the hallmarks: an extremely dodgy abstract, poor punctuation (as described above in comments), ropey spelling, dubious use of English (whassiss "immortal"?) and poor LaTeX skills.

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

Check the last link in the summary. The author is a highly-respected mathematician in the field and this follows previous work that has been peer-reviewed. That doesn't mean it is *right*, but that does make it newsworthy.

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

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

Hokay, missed that. All the same, I'd wait for final verification before breaking out any bubbly (and then proceedng to analyse its egress from bottle to glass).

Shoehorning in my field (1)

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

Can I just say "As a mathematician/engineer/chef," to get modded up now?

Re:Shoehorning in my field (1)

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

Hmm, a Mathematician chef would probably be able to make one hell of a pie at least. :)

What millennium? (0)

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

Since these "millennium problems" aren't problems that have plagued mankind for an entire millennium, and they probably won't even last a whole millennium until they're solved... what exactly is the point of calling them "millennium problems"?

Last claim of sexists falls (-1, Offtopic)

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

The last refuge of modern sexists is the claim that even if men and women have the same average scores, men have a greater variance and therefore are more likely to produce the very top level mathematicians and scientists. For an example of the debate see Pinker vs. Spelke [edge.org] , or one could also read Dr. Elizabeth Spelke's papers [harvard.edu] including Sex differences in intrinsic aptitude for mathematics and science: A critical review [harvard.edu] .

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 plural of anecdote is not data?

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)

Great!

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)

As the slashdotter above me stated...

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...

...Waitaminute. (0)

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

Holy shit holy shit holy shit holy shit holy shit what? NS solution? Jesus Christ. Awesome!

Penny Smith's usenet posts! (2)

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

I read her very entertaining posts [google.com] for many years, until she suddenly quit killing time on Usenet.
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