/sci/ - Science & Math

>>6284959
i want to believe…

>>6284959

The wikipedia article has a link.

http://en.wikipedia.org/wiki/Millennium_Prize_Problems#cite_note-5

After some searching, I believe this is the paper:

http://www.math.kz/images/journal/2013-4/Otelbaev_N-S_21_12_2013.pdf

How much longer to Riemann?

It's the only one people actually care about anyway.

What are the applications?

>>6284992
Nah bro, this is the Riemann Hypothesis for non-mathematicians scientists.
This is going to have huge consequences.
Go Kazakhstan!

>>6285003
Greatest country in the world.

Poincaré, solved by a Russian mathematician.
Navier-Stokes, potentially solved by a Kazakh mathematician.
Is this the revival of the USSR's former glory?

>>6284992
http://www.academia.edu/350005/Proof_of_the_Riemann_Hypothesis

>implying Navier-Stokes was a hard problem

I solved it when I was a kid. I considered the proof too trivial to publish.

>>6285020
Go to bed Gauss.

>>6285020
Get back to your window, Jacob.

>>6285013
it's just that american money can't buy everyone that didn't have a shitty upper education

Never been more relevant.
https://www.youtube.com/watch?v=dIV-QdPEx-Q

>>6285038
mathematics is the best here, kazakstan

>>6284959
WOW! If this is true, it's the biggest news of 2014 and we're barely in January!

So when will there be an explanation of what Poincare/Navier-Stokes means to the layperson?

>>6285056
http://theconversation.com/millennium-prize-the-navier-stokes-existence-and-uniqueness-problem-4244

>>6284987

"Well, I guess I'll take a look at it. I probably won't get any of it, but who cares"

> Open paper http://www.math.kz/images/journal/2013-4/Otelbaev_N-S_21_12_2013.pdf

Seems like I was right

>>6285056
The paper has been linked ITT. What part of pic related do you not understand, pop sci fag? Did you fail calculus?

>>6285075
>>6285079

I've been looking at it for the past 10 min or so… ever since it was posted, and even through I'm a mathematician, i do not speak Russian so I can't really try to understand it. But I can tell you from looking at the equations and following few proofs that the guy is definitely not a crank. This is not some non-sensical bullshit or some schizo proof writing. He does show rigor.

There could be something to this.. but it needs to be translated to english.

>>6284959
more importantly, is this bullshit? I can't find any sources that seem to not be bullshit. Other than his paper, of course, and I unfortunately cannot read russian.

>>6285084
are you sure? I mean, the paper looks acceptable as far as I can tell (not that far, given my russian) but all the articles don't really bother to check if this is bullshit.

>>6285103
>russian
It's not Russian

Why would this be bullshit ?
What's so hard to believe ?

Very nice!

Oh yes.


OH YES!

>>6285105
because he isn't well known and it would be suspicious if he solved it without major new ideas.

>>6285104
>>6285104
is it in Kazakh? what the fuck?

>>6285114
>because he isn't well known and it would be suspicious if he solved it without major new ideas.

Suppose you have a set of all very skilled mathematicians and scientists and another set of all well known mathematicians and scientists. Their intersection is tiny. In my opinion it would be more unexpected for the proof to be produced by someone like Michio Kaku or NDT.

>>6285079
I failed russian, asshole.

>>6285145
or any retarded language using this stupid ugly alphabet

>>6285103
>but all the articles don't really bother to check

LOL… where the fuck have you been for the last 10 years? journalism is shit. they don't check anything even if they can understand it.

problem is that this is a 100 page dense mathematical paper written in russian so the number of people who could check it is quite small. maybe Perlman will take a look.

>>6285134
I'm suspicious that he can't get a position in Russia - if he were at Moscow State or Leningrad it would be different. I agree about Kaku and I realize the need to not just dismiss this guy (this very well could be correct; he isn't a crank as far as I can tell), but I also don't have high hopes.

i only care about fermat

>>6285151
>this is a 100 page dense mathematical paper written in russian so the number of people who could check it is quite small
I know the Russians used to be good at analysis, so I would guess there are a number of people who could check.

>>6285158
Navier-Stokes implies Fermat, idiot. Where have you been? The <span class="math">\epsilon^2[/spoiler]-conjecture is widely known.

>>6285024
lel'd

So… if Navier-Stokes is solved, what's the next big Millennium Problem to fall? Anyone have some insight?

I'm willing to bet that P=NP will never be solved by humans.

>>6285211
P=NP will never be solved by humans.
The Birch and Swinnerton-Dyer conjecture will be next, I predict.

>>6285134
Pretty sure he meant "well known" as in within the academic mathematical community, not as in pop science.

>>6285325
>well known

Otelbaev has published in some very respected journals, and trained with the very top people. His work is worth serious scrutiny. Of course, it is easy, even for the most brilliant scholars, to make a mistake which makes it look as if a big problem has fallen. Skepticism, but no mockery, please.

http://otelbaev.com/?page_id=16

this is gonna be good stuff for the future, think of perfect fluids/weathers/structure resistance simulations as well as new forms of propulsions

>>6285079
I'll be honest, giving the basic definitions in the paper isn't the best sign. Not that that alone means that it's crank-work, but it is one characteristic thing.

Someone have a source?

This is huge.

>>6285423
>http://www.math.kz/images/journal/2013-4/Otelbaev_N-S_21_12_2013.pdf
There is an one page abstract in English at the last page.

>>6285435

Only been submitted to the Kazak journals so far? How come it's not getting attention?

I am quite sceptical. For some odd reason there have been quite a few claims about solving the NS equation in the last few months. I recognize that this is a reputable mathematician with respectable credentials but that paper has been in circulation since late 2012. I am open to being proven wrong though.

A shame really.

So, what are the implications of such a solution? When can I expect my hyperdrive?

>>6285460

CFD software will be able to operate in an unbounded state without having to take any approximate errors into account. Essentially, the problem is that nowadays all fluid dynamics errors are modelled by approximations. Proof of NS gives us the criteria such that we can assume unbounded finite solutions over the entire defined axiomatic region while eliminating truncation errors.

>>6285477
>CFD software will be able to operate in an unbounded state without having to take any approximate errors into account. Essentially, the problem is that nowadays all fluid dynamics errors are modelled by approximations. Proof of NS gives us the criteria such that we can assume unbounded finite solutions over the entire defined axiomatic region while eliminating truncation errors.
.
the fuck are u talkin about


how does this help the average joe

>>6285487

this. will bread be cheaper?

>>6285166
>Navier-Stokes implies Fermat
Looked this up and got nothing.
Can you give me a source please?

By the way, not the guy you're responding to.

>>6285487
okay so layman's terms

there are a bunch of equations that model fluids (the NS equations)

it is an open problem whether those equations have solutions for every possible input, and whether the curve is smooth

right now we solve NS by approximation. if both are true, then the quality of our approximations will increase dramatically

>>6285493

>will bread be cheaper?

I lol'd.

>>6285497

This is a reasonable explanation. I maintain my scepticism about the proof however.

>>6285495
It was a joke.

>not getting the epsilon^2 joke

Taking bets on the next Millennium Problem to be solved.

I'm thinking Birch + Swinnerton-Dyer will be next. Too much advancement in algebraic geometry recently to let that go for too long.

As for the others, the order in which they will probably solved:

1. Poincare (2006)
2. Navier-Stokes (2014)
3. Birch & Swinnerton-Dyer (???)
4. Yang-Mills (???)
5. Riemann (At least 2050)
6. Hodge (???)
7. P vs. NP (Possibly independent of current axioms/impossible/etc.)

>>6284959

Let me know when reliable sources are reporting that the proof has been checked and accepted.

Pretty sure dozens of people have claimed that they've proved Millennium Problems, and only one of those claims so far hasn't been bullshit.

>using "grad" and "div" instead of the shitty nabla operator notations

Based

>>6285635
i like your optimism wrt Riemann! I don't think we'll see it solved by 2200 but hope I'm wrong. As for P=NP… never.

>my sides when he's a fucking pleb who uses < and > instead of \langle \rangle

>>6285663

I agree, I can barely look at that equation without wincing.

>>6285663
>idiotic ad hominem

please kill yourself.

>>6285663
LOL

Maybe one day his proof will be as good as my proof of NS!

>>6285663
this is hilarious

>>6285497
>right now we solve NS by approximation. if both are true, then the quality of our approximations will increase dramatically
So... we'll need less computer time to arrive at a precise enough solution or what? It's not like computer time is expensive or anything (unless it's a billion times more efficient or something). It doesn't seem to have any interesting properties except woo we solved another PDE.

2013 - Year of Number Theory (Weak Goldbach proven unconditionally, along with major advances towards Twin-Prime Conj.)

2014 - Year of Physics (Navier-Stokes... ???)

>>6285692
>Weak Goldbach proven unconditionally
Whoa, sauce?

>>6285697
Search the internet? This was early 2013/even late 2012 when a serious claim was made at it.

>>6285692
Navier Stokes is an engineering problem.

>>6285684

Run a CFD simulation and you will understand just how critical this is.

>>6285702
Lel, as a part of my uni application I made an essay about an approach to solving Goldbach's by discovering a function of x giving the number of pairs of primes p+q=x, where x is an even integer. Unfortunately, function is very accurate for calculating total number of pairs for, say, x,x+1,x+2, but not very good at predicting the specific value for x. It converges slow as shit. Anyways, it's O(actual number of pairs), so when somebody proves that constant A must have a minimal value, goldbach's will be proved for all x where A*f(x)>1. I've found a really neat value for A, but I can't rigorously prove it's the smallest value so I'm kinda screwed there. Whoever does that will prove Goldbach's.

https://en.wikipedia.org/wiki/Abc_conjecture

http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html

Thank you japan-san you are my greatest ally

>>6285715
Not even shittin you, red is my function, green is a function fitted to the data points.

>>6285726
Oh boy Mochizuki.

Let's get this shit started.

>babby's first inter-universal Teichmuller theory

>>6284959

and this is the sort of thing that we pay our "greatest" minds to work on? honestly, if a scientist/mathematician can't actually work for a business and make USEFUL contributions instead of all this waffling then this world would be better off

>>6285766
This is incredibly useful you fucking pleb

>>6285715
>inb4 a 4channer solves goldbach's conjecture and we are overrun with math phd newfags

>>6285766
2/10

>>6285777
Yay someone can finally do our homework

>>6285777
crowdsourcing can do anything tho right?
nice trips

>>6285777
>4chan user
>solving Goldbach's

>>6285777
Good, maybe they will push out the "does .999 = 1" fags and >tfw less than 170 IQ fags.

>>6285766

This does have practical benefits. Video games can now have realistic water effects with more than 3 bad guys on the screen at one time. The HD edition of Bioshock is going to be sweet.

>>6285790

>>6285777
>y2k13+1
>caring about goldbach
>ISHYGDDT

>>6285497
Explain. How will your code change from knowing existence and regularity? Isn't there code out there that assumes this already?

What makes you guys say one problem is harder than the other? Progress already made?

Why is Riemann and P = NP so much harder than the others?

>>6285079

>BEKTOP CKOPOCTN

>>6285940
Riemann because it's probably the most famous of all seven (among mathematicians) and arguably one of the most far-reaching and influential conjectures of all mathematical history, especially in number theory (though Fermat had much more influence purely in NT, Riemann has more overall). Zeta function are ubiquitous in all major fields including complex analysis, number theory, algebraic geometry, and more. Curiously enough, these generalized zeta functions are sometimes easier to study and prove theorems about (see: the Weil conjectures, etc.), but their prototype's infamous property - the Riemann hypothesis - remains resistant to proof. It has also been conjectured that the distributions of zeros of the Riemann zeta function (which correlate directly in a sense to the distribution of prime numbers) are related to energy levels of heavy nuclei - implying a very deep romantic connection between the prime numbers and the foundations of our universe.

As for P vs. NP, it's notorious because of its almost borderline philosophical nature, and the fact that people really don't have a clue on how to even attack it. Even Riemann has been attacked in a multitude of ways with some interesting results, but P vs. NP doesn't really give any clues on where to go. If you read up on some simpleton explanations, you can see that in some sense if P = NP is true, then "solving" a problem is about as difficult as "verifying" a problem is true. Now how would you even begin to address such a conjecture? The implications of such a statement are incredibly deep.

>>6285947
That means velocity vector.

>>6285955
Humans simply don't have the capacity necessary to grasp the complexity of trying to prove or disprove P=NP. What's actually amazing to me is that we, humans, actually managed to discover and pose one of these super-hard problems. Rest of the Clay math problems at least seem approachable at the surface and you get a sense that you could solve some of them… but not P=NP.

>>6285955
I wonder if physical phenomena can ever be used to prove one of these superhard problems. Like it would be awesome if a conjecture being true would imply a certain physical phenomenon would happen. But if it's observed to not happen, then the conjecture is therefore false.

Proof by physical contradiction!

Could someone explain in layman terms the P=NP problem? Why would it be so much difficult to solve than the other Milennium problems?

>>6286034
Probably because it's unsolvable and impossible to prove that it's unsolvable.

>>6286034
From Clay Math:

Suppose that you are organizing housing accommodations for a group of four hundred university students. Space is limited and only one hundred of the students will receive places in the dormitory. To complicate matters, the Dean has provided you with a list of pairs of incompatible students, and requested that no pair from this list appear in your final choice. This is an example of what computer scientists call an NP-problem, since it is easy to check if a given choice of one hundred students proposed by a coworker is satisfactory (i.e., no pair taken from your coworker's list also appears on the list from the Dean's office), however the task of generating such a list from scratch seems to be so hard as to be completely impractical. Indeed, the total number of ways of choosing one hundred students from the four hundred applicants is greater than the number of atoms in the known universe! Thus no future civilization could ever hope to build a supercomputer capable of solving the problem by brute force; that is, by checking every possible combination of 100 students. However, this apparent difficulty may only reflect the lack of ingenuity of your programmer. In fact, one of the outstanding problems in computer science is determining whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. Problems like the one listed above certainly seem to be of this kind, but so far no one has managed to prove that any of them really are so hard as they appear, i.e., that there really is no feasible way to generate an answer with the help of a computer. Stephen Cook and Leonid Levin formulated the P (i.e., easy to find) versus NP (i.e., easy to check) problem independently in 1971.

>>6286060

Verification program that travels through time. Fields Medal and million dollars please.

>>6286034

This is something people generally spend an entire class on at the graduate level in computer science, if they're going the theoretical route of study. It's part of something called complexity theory.

See, each algorithm has a definite upper bound on runtime, as the problem size, n, increases.

An algorithm in P (which stands for polynomial time) is guaranteed to solve problems of a certain type in time no greater than n^x, where x is some power, and n is the problem size.

All problems which can be solved by algorithms in P can also be solved by algorithms with much worse upper-bound (worst case) performance.

So, by the previous statement, there exists a class of algorithms that can solve some problems in time greater than polynomial. This space of problems is called NP (for non-polynomial) and consists, of, well, algorithms that run in greater than polynomial time. Most people assume exponential (in the size of n) or more, but we don't really know for sure unless a proof exists.

Now, there are these other problems that are called NP-complete. A problem in this class is reducible to every other problem in this class by either the Cook or the Karp method (many-one reducibility or the other kind, I forget what the other name for it is, I'm drunk). What *this* means is a problem solvable by an NP-complete algorithm, with certain translation, can be also solved by every other algorithm in the NP-complete class.

If P = NP, every algorithm in NP-complete automatically becomes solvable in polynomial time. This is absolutely *huge* because the RSA algorithm, which enables ssh, financial transactions, and tons of other shit, is NP-complete on the decoding end.

If P = NP, a huge mass scramble will have to occur all over techdom to keep money, privacy, etc. in check.

If P != NP, as is suspected, life continues as normal and we can't solve problems that are in NP but not in P with algorithms that are polynomial in terms of n, the problem size.

>>6286060
So what I'm getting is, if I have a solution to a problem that I know is correct, could I calculate that problem and get that solution?

>>6286072
>could I calculate that problem

that's where the complexity lies. yes, you can easily verify whether your solution is correct or not but getting that solution is what's hard.

think of the encryption that we use today. you can easily verify whether the key you've used for decryption is correct (you'll either get some text in english as a result or you'll get garbage if the key is wrong). but devising that key from the encrypted message itself is hard.

>>6286060
>Stephen Cook

True story: after Cook got his PhD from Harvard, he went to Berkeley and taught there for few years and was DENIED tenure. He then went to University of Toronto and formulated P=NP and wrote few other extremely influential papers. He's now one of the most important computer scientists alive.

Way to go Berkeley!

>>6286068
>using RSA as the main reason why P = NP would cause an uproar

Where have you been? Have you been following the NSA leaks? There is reason to suspect that the NSA already has a quantum computer, making RSA child's play to crack.

>>6286081
Another reason that "elite" schools are bullshit.

>>6286115
>There is reason to suspect that the NSA already has a quantum computer, making RSA child's play to crack.

You're an idiot. NЅА's quantum project has such a small budget that they're not even competitive with European labs.

Odds that anyone today has a working quantum gate computer are exactly zero.

And if those Snоwdеn docs have shown us is that NЅА's cryptanalysis is on par or slightly better than academic world and that they rely on stealing keys and backdooring products not breaking cryptography.

>>6286125
And those docs were dated over 5 years ago.

5 years of top top secret government research can easily translate into decades of world-class academic research. Regardless, anyone who uses RSA today is an idiot. OTPs + private keys are the only way to go, and the only way there ever will be.

How long until the peer reviews come in?

>>6286134
About 5-10 years.

That's how math goes.

>>6286128
>And those docs were dated over 5 years ago.

No, only some were dated that old.

If NЅА broke RSA, they wouldn't have to do any of the shit they're doing today and are exposing themselves to scrutiny. They also wouldn't have to be spending all that huge budget on building Utah supercomputing center.

We won't have a working quantum gate computer for the next several hundred years… if ever. Problems with noise are just incredibly complex that even if they spent all of their budget on building QGC, they still wouldn't be able to make one for the next 50+ years.

>>6286125
Trying to tell people that things cost the government money too is pointless. They just assume the government can just wave a magic top secret research wand and poof you get James bond shit out of nowhere.

RSA was top secret information before it was publicly "discovered" by its namesake mathematicians.

Who is to say that a top secret method of breaking it has not been recently discovered? You think they'd just come out an publish that shit? No. The reason they don't give a fuck about the leaks of them putting backdoors in RSA stuff is to make the public think they have no clue how to crack it - to entice the public to keep using it and hence keeping their frontdoors wide open.

>>6286157
>RSA was top secret information before it was publicly "discovered" by its namesake mathematicians.

It was discoved by a brit and they haven't done fuck-all with it.

>Who is to say that a top secret method of breaking it has not been recently discovered?

Leaked docs don't indicate it. And what they do indicate is that math is hard. They can easily break Tor, for example, if they could factor large numbers. But they can't.

>>6284959
I can prove fermat's theorem im 2 steps

>>6285354
>Skepticism, but no mockery, please.
this seems to be the fair approach

>>6285410
yeah. It actually isn't as bad on other counts, but then I'm possibly missing some because I don't know Russian

>>6285445
>Only been submitted to the Kazak journals so far?
I mean, this seems to be one of the big flaws. It's a real journal, though perhaps not suited to a discovery of this magnitude. Also, I'm surprised they didn't rush it through or get outside experts to comment.

>>6285663
you're kind of obnoxious and petty, but actually reading the paper is pretty good for /sci/

The problem is that nobody knows Russian here (or whatever language the paper is written in), so we can only speculate about the paper. Someone has to translate it, so the paper can be judged.

So if I'm understanding this right - he's been able to demonstrate that the NS equations are solvable for any 3D flow and that the mathematics he's developed to prove the solution may make it simpler to determine analytical solutions for any arbitrary flow.

Right?

Because if so that's definitely huge. One of the major obstacles of fluid dynamic simulations is that everything has to be approximated and modeled numerically and algorithmically. If obtaining anayltical solutions for any flow is possible and this guy's process makes the process of obtaining a solution simpler, than we could model fluid systems with no approximation or numerical solving.

>>6286184
Layman here,
if math is a universal language, shouldn't a competent mathematician be able to look at the equations in the paper and determine if it works or not?

>>6285635
You're overly optimistic about Navier-Stokes being correct and overly pessimistic about the Riemann hypothesis. We have no idea when it will be solved.

>>6285684
computer time is expensive when it comes to fluid dynamics. In fact, there are many fields where it is difficult.

>>6285079
This is proof the paper is correct. The only other paper that does this is
http://arxiv.org/pdf/math/0211159v1.pdf

>>6286194
They could make a educated guess, but nothing more. You don't write pages of text if it's useless.

>>6285726
I mean, that's actually got a decent claim at things. This one... less so.

>>6285777
this board shitposts worse than /s4s/, I doubt anything could make it worse.

>>6286194
Have you ever had a teacher who told you to show your work, even when you had the proper solution written down?

>>6285777
I would be okay with this

>>6286208
Well, I'm assuming he showed his work in this paper. And in any case, if he gives the solution and you know what to use it for, shouldn't you be able to determine if it works or not?

>>6286194
Language explains the process, methods, assumptions, and rationale behind the math.

I'm sure if we had a math PhD who specialized in very similar areas of study they could potentially make sense of it but otherwise it's like trying to cook a souffle based on a cookbook in chinese with only a few snapshots of the ingredients and mixing bowls to go on.

>>6286001
that would not be a mathematical proof because we aren't 100% sure of the underlying physics. The theory could just as likely be wrong.

>>6285955
>in some sense if P = NP is true, then "solving" a problem is about as difficult as "verifying" a problem is true
which is why is it likely false, although it is fairly surprising that a proof of that is so hard.

>>6285992
>Humans simply don't have the capacity necessary to grasp the complexity of trying to prove or disprove P=NP
wait until we have something. This is not a rigorous statement.

>>6286166
>he believes that Tor is safe

Don't be an academic retard and actually learn some things about technology. >>>/g/ Many Tor exit nodes are compromised.

>>6286213
And in any case, if he gives the solution and you know what to use it for, shouldn't you be able to determine if it works or not?

Given enough time, I could decipher the Russian as well.

>>6286199
>pessimistic regarding Riemann

If you think it has a chance on being proven within even 20 years then you probably don't have much experience in math.

>>6286068
one of the other things is that verifying a proof (which is polynomial) and writing a proof would become just as easy, so if the proof of P=NP were constructive (best case scenario), all the other millennium problems would also be solved.

>>6286231
>P=NP implies all other conjectures ever

>>6286226
>Don't be an academic retard and actually learn some things about technology. >>>/g/ Many Tor exit nodes are compromised.

http://www.informationweek.com/traffic-management/nsa-battles-tor-9-facts/d/d-id/1111857?

>>6286238
The "Tor Stinks" doc leak was from many years ago. Your article even proves that the NSA is actively working on dismantling it, and were successful already in some cases.

Bottom line: if the exit node isn't safe, you ain't safe. If you end up coming out of an NSA node, you're screwed.

>>6286128
>5 years of top top secret government research can easily translate into decades of world-class academic research
lolno. The NSA is around 7 years ahead of academia. The don't do any sooper-sekrit bullshit, especially not in number theory.

>>6286243
>NSA
>not interested in number theory

Has the shillbot even reached /sci/?

>>6286244
Fuck of /pol/. We have to deal with enough of your shit already without you fucking up the few legitimate threads there are

from thread

>>6286235
well, no, it just lets us determine whether they are true. And that also depends on the constants being small enough - if it maps a verification algorithm to another algorithm which is O(n^112002300320) that isn't very useful either. Hell, even the constant term could fuck things up if it were, say the number of elements in the monster group (at least for the foreseeable future)

>>6286248
You do realize that page you're trying to translate appears in English at the end of the paper, right?

It gives a very broad idea of what is proven in the paper but doesn't give any details about the methodology or the exact nature of the solution. We're probably just going to need to wait for a translated version of the paper to be released.

>>6286244
>Has the shillbot even reached /sci/?
1) No one would care to shill on this shitposting hellhole
2) I wrote unclearly. What I mean is that the NSA doesn't do much amazing research because they don't attract the top talent - the top talent goes to Academia, where they get accolade, or leaves like Grothendieck. No one wants their life work to be completely secret, and those who are motivated by the math itself tend to avoid political affiliations. So it is unlikely some super-genius is being employed by the NSA right now.

>>6286247
>he doesn't know the shillbot is a real thing

I would paste the copypasta proof, but I'm sure a quick search in the /g/ and/or /pol/ archive would lead you right to it. It's not some le ebin maymay from /pol/; it's been caught in the act with piles of evidence documented.

>>6285663
\lange and \rangle do look prettier, but it's a lot more effort to type than < and >, plus it makes your latex source incomprehensible.

>>6286255
>doesn't give any details about the methodology or nature of the solution
Well that's suspicious as fuck.

>>6286283
That's probably in the other 99 pages of the paper.

>>6286295
>100 pages to prove a Millennium Prize Problem

I'm calling bullshit. That's too little.

>>6286298
Why?
If P=NP then a minimalist proof could be 1 or 2 pages.

>>6286300
But P =/= NP.

>>6285157
>Leningrad
Oh, you.

>>6286302
Prove it

>>6286302
Show your work, claim the prize.

>>6286308
>>6286309
If P = NP then there would be a simple proof of this fact. However, no one can prove it simply. Thus P =/= NP.

>>6286311
1/10

>>6286056
>impossible to prove that it's unsolvable.
Has someone proven that there are statements that are unsolvable and impossible to prove unsolvable?

>>6286475
>X exists but we can't find specific examples of X without contradicting our premise.

I wonder if there's a name for that type of conjecture.

>>6286475
yes?
Gödel's first icompletness theorem gives the existence of such statements.

>>6286494
How? It says there are undecidable statements, but some for some undecidable statements it is proven they are undecidable. But can you prove it for every undecidable statement?

>>6286475
continuum hypothesis:
proven to be impossible to prove or disprove.

>>6286068

> This space of problems is called NP (for non-polynomial)

It's actually non-deterministic polynomial. Pretty easy to explain once you learn some basic automata theory.

As for P vs NP, I think it's most likely going to be solved by a computer of some sort.

It's probably worth mentioning that although NP-hard problems are generally...well...hard, people have still been able to create some pretty interesting and good solvers. Travelling salesman would be a good example, branch-and-bound based solvers can obliterate TSP on some relatively large datasets if they're implemented properly (giving exact, optimal solutions).

I'm doing my intro to fluid dynamics next semester. If this is going to make my knowledge obsolete in a year, I am going to be royally pissed.

>>6286503
Right but the time required to solve them still increases exponentially so there is a limit where a very long amount of time would be required to solve very large TSP problems even with branch and bound.

>>6286555

True, no doubt in that

>>6286494
no, but there we can prove some things are unsolvable.

>>6286550
Guess you are going to have to ask your professor to take a look at the paper.

>>6286550
Even if Otelbayev's proof proves valid it will not make much (if anything) of what you'll learn in an intro fluids class irrelevant. The paper is attempting to prove that smooth solutions exist for the Navier-Stokes equations for any arbitrary three dimensional flow. This would mostly impact how we solve more complicated flows, how we analyze problems like turbulence, etc.

Most of what you'll go through in an intro fluids class are exact NS solutions for 2D and simple 3D flows, looking at viscosity, vorticity, circulation, deriving the Bernoulli equations, waves, etc. Some classes will also do short chapters on aerodynamics, and if you're very luck you might even get to cover a little bit of shock physics.

>>6286499
yeah, but you're still wrong because it was possible to prove it was unsolvable.

I don't get it, couldn't P = NP only and only if N = 1 or P = 0? It depends on the values, right?
Must tell us first!

>>6287040

exactly, this isn't binary

not 0 or 1

this is math

AND IT DEPENDS!

Why does it need a 100 page proof?

Isn't it pretty easy to verify whether a PDE is satisfied by a particular equation?

Not impressed

>>6287080
Showing that the NS equation is satisfied for a particular flow is easy. Proving that the NS equation will yield a smooth solution for ANY flow is not.

Hence the 100 page proof.

>>6287040
I am stealing this proof

I'm experimentalist in fluid dynamics.

If the paper is right, I'll be obsolete in couple of years.

:(

>>6286001

Even if we knew the physics behind an event, observing it not happening doesn't prove anything. Null hypothesis, bitch.

>>6287040

2 l8 4 b8 m8

He states the problem as having zero initial condition and in a periodic cube. The non-triviality comes from arbitrary L_2 external force.

Aren't arbitrary domain and initial conditions required for the millennium prize? I suppose you could get rid of the domain problem by some transformation (I'm not a mathematician) but can arbitrary force account for arbitrary initial conditions?

>>6287109
Isn't that like saying "solving a particular simple harmonic motion differential equation is easy, solving ANY SHM differential equation is not"?

I mean if he has a general solution for solving NS equations then why is it not quite straightforward to show his solution satisfies any equation of that form like it is with simple harmonic motion?

>>6287167
Existence can be shown non-constructively. If you ever took a math course, you'd know this. Please do us all a favor and invest more time into your education and less time into showing off your ignorance on 4chan.

>>6287162
Should have checked the wikipedia first...
http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness#Statement_of_the_periodic_problem

Assuming it's right, there are two prizes : for unbounded space and for periodic cube. Both are required to have arbitrary initial conditions, so I don't think he's getting the million. Still, if his proof is correct for this problem statement he must be close as fuck.

>>6287167
You are an actual, real idiot. Please, if you don't understand what existence, uniqueness and smoothness of solutions to differential equations mean and why they are important in mathematics then STOP COMMENTING.

>so I don't think he's getting the million. Still, if his proof is correct for this problem statement he must be close as fuck.

This made me realize that the prize money might be an incentive to not share partial solutions for these problems.

>>6287173
>Existence can be shown non-constructively.

Exactly, which is why he if he's solved all NS equations he should be able to state their general form the same way you can with any other kind of solved differential equation.

Is this hard to understand?

Have you never solved a differential equation before, kid?

>>6287177
I know full well what those are. You, however don't seem to know what the word "solve" means.

>>6287284
You are either a troll or sufficiently retarded to sound like a troll. In both cases you're not welcome. Please leave and don't ruin one of the very few good threads we have on /sci/.

>>6287284
>doesn't understand what "non-constructively" means

Are you verbally deficient? Have you been diagnosed with a neurological disorder?

>>6287289

Why did you disappear from this thread?
>>6287029

>>6287133
If you were really an experimentalist in fluid dynamics you wouldn't believe that.

Even if the paper is right it only proves what we already assumed about the Navier Stokes equation.

There will always be more experiments to run, more theories to try and validate, and so on.

>>6287280
Would you share a partial solution otherwise?

I wouldn't.

>>6287338
If you care more about advancing physics and mathematics than prize money you might.

What is the impact behind Mochizuki's alleged proof on the ABC conjecture?

>>6287351
There is none. Number theory has no applications.

>>6287354
>Number theory has no applications
Doesn't it have applications within cryptography?

>>6286068
>This is absolutely *huge* because the RSA algorithm, which enables ssh, financial transactions, and tons of other shit, is NP-complete on the decoding end.
even if P=NP, we still don't have a clue, how to construct an algorithm that does that solves the problem in polynomial time.
also we don't know about the coefficients of the polynomial.
2^n is still more attractive than n^10000

>>6287354
>Number theory has no applications.

>someone this retarded posts on /sci/

why am I not surprised anymore?

>>6287361
>>6287381
>on 4chan
>doesn't understand trolling

Y'all niggas need to educate yoselves
>>>/b/

Stupid question here. If that is such a groundbreaking proof then why haven't I read anything about it? (Of course they need to check the correctness) But isn't that worth a newsflash somewhere (wikipedia etc.)?

So how long before it's verified ?
Can't a PDE expert like Cédric Villani check this shit ?
Isn't it a "big thing" ?

>>6287311
He did not define his terms.

If he was satisfied with his "proof" then good for him, but the fact remains that he utterly failures to prove that my proof was wrong.

It looks like he was a plodding theory-learner who got so caught up in reading Wikipedia pages on advanced mathematics that he forgot the significance of one of the most fundamental properties of the integers: closure under addition.

Basically the equivalent of a pop-mathematician.

>>6287390
>lel I was only pretending

>>6287418
You are too uneducated to understand his post. But in your words it doesn't matter because truth is truth irregardless of whether you understand it.

>>6287390
if you think every idiotic post on here is trolling, you're just as big of an idiot as them.

ever met an average intelligence person? do you know how stupid they are? 50% of people are even stupider than them. and yes, many of them post on here.

>>6287426

>irregardless

>>6287426
Which is exactly what I said.

He could draw a picture of a duck and call it a proof , and if he's satisfied with that then good for him.

But the fact remains that I've already proved the result incorrect and he was unable to disprove my proof.

>>6287433
He totally destroyed your fallacious bullshit.

>>6287434
No he didn't, he neglected my own mathematical argument and produced his own undefined argument.

>>6287468
His argument addressed yours. Please don't come back until you have the education to understand it.

>>6287408
1) It's new.
2) It's 100 pages of dense mathematics.
3) It's all in Kazakh or Russian (not sure).

Big proofs like this need to be carefully peer-reviewed. If it's confirmed, it will be big news.

>>6287348
I don't care about the prize and I don't care about advancing mathematics if I'm not the one doing it.

Don't anyone else think this way?

>>6287791
>Don't anyone else think this way?

You remind me of this crazy nutjob's writing.

>>6288260

*shrugs*

>>6285013
USSR strong

>>6284959
>completed
>not peer reviewed

big fucking whoop

>>6288260
That's bad and I now feel bad.

Navier Stokes problem is the millennium problem that I'm most interested in. Now it's over for me, I don't have a chance to be the first person who solve it. Feels bad man.

>>6288260
You're confused.

This is 4chan. No one will upvote you for shoehorning a shot at Ayn Rand into the discussion.

>>6288529
You sound like one of those pseudo intellectuals who try their best to be above comments on an Anonymous web forum.

>>6285005
potassium number one export product

>>6288478

>implying

j/k anon

any updates?

So… any news?

>>6285104
>>6285116

It's Russian. Kazakh uses some different letters that I would recognize immediately. This is straight Russian Cyrillic.

>>6285001
It's frequently cited in Fluid Dynamic classes in engineering, which often simplifies the problem with assumptions.

>>6285300
"P=NP will never be solved by humans"

I'm pretty noob so excuse my ignorance, but why would that be? Beyond the limit of human reasoning?

>>6291859
because we have no idea how to even approach it.

>>6288478
The unbounded domain case is still open. Go for it champ.

>>6291688
Honestly though, the problem was mostly academic and everyone assumed the existence, uniqueness and smoothness for quite some time. I haven't read the proof, so I don't know what he did (assuming he's right) but the biggest problem physicists and engineers face is to model (physically and numerically) turbulence in some simple yet meaningful way.

The millennium problem, by itself, is just that the problem as mathematically stated is not nonsense. Mathematicians, I presume, hoped for some nifty new ways of approaching non-linear PDEs in general.

At any rate, we already know that physically N-S equations do not describe nature entirely accurately. No fluid is entirely linear, the continuum hypothesis can be stretched quite thin in some cases, the incompressible N-S equations (for which the millennium problem is stated) are often useless in aerospace engineering plus there's such things as disregard of relativity or possible quantum effects at very small length scales.

>>6290612
>>6288991
i could translate some of it if you guys want

>>6292753
That means nothing really...

>>6292885
yes
translate all of it

>>6292902
all right i'll do some of the beginning that hasn't been done yet

okay guys.
I'm not a mathematician, but I'll ask /int/ if they can translate the document.

>>6292933
okay here is the /int/ thread.
>>>/int/19300360

As a geophycsics masters student who fiddles alot with numerical simulations involving mantle convections, this pleases me.

>>6292943
I thought you were volunteering to translate it?

>>6292885
here is an open "project" going on to translate it, I'd go from there:
https://github.com/myw/navier_stokes_translate

here what's readable already:
https://github.com/myw/navier_stokes_translate/blob/master/article.tex

>>6292959
I'm not a russian.

>>6292959
no that was me

>>6292963
I'm missing something
What does
<div class="math"> \int_Q p(t,x) \mathrm{d} x= p_0, p_0= \mathrm{const} > 0 </div>
mean or how did he get it?

Also since you uprighted some of his operators, wouldn't it be prudent to upright his other operators: <span class="math"> dx=\mathrm{d} x [/spoiler]

>>6293018
>Also since you
I take no credit for anything there. My flatmate is russian (pretty much a bitch) but I can only say what sounds like "da", "dag" and "ygrid".

>>6292963
well damn i guess what i'm doing is pretty much useless then
i'll contribute to this project instead

>>6293030
thank you for translations!!!!

>>6285020
sooo.. which is the hard problem?

>>6293219
Riemann, of course.
P = NP impossible, because P != NP

>>6293272
>P = NP impossible, because P != NP

oh you idiot. do you even know what a proof is? go disprove it if you think it's easy.

>>6285079
>What part of pic related do you not understand, pop sci fag? Did you fail calculus?

ΦedgyΩme

>>6293285
But what's the point?

>>6285079
calling <span class="math">\Delta [/spoiler] the Laplace operator instead of <span class="math"> \nabla ^2 [/spoiler].
It's simple as soon as you see the translated, but without it...

>>6293285
I never mentioned that it is easy to prove. The most obvious facts are the hardest things to prove and sometimes even impossible to prove. Mathematicians call them axioms. Probably, P != NP will be an axiom one day.

>>6287167
The first primes are 1, 2, 3, 5, 7

Holy shit this proves that all non-2 primes are also odd numberse

>>6293398
Yes, it is. According to definition even numbers can be divided by 2. So, the only prime number which can be divided by 2 and be prime at the same time is 2.

>>6293398
>1, 2, 3, 5, 7
>1, 2, 3, 5
>1, 2, 3
>1, 2
>1
>1
>1

>>6293408
You completely missed the point. Just showing a trend in the first few primes, or picking a couple random primes and showing they're all odd, isn't proof that (almost) all primes are odd. Did you eat paint chips as a child?

>>6286260
>it is unlikely some super-genius is being employed by the
pray to god they don't get there hands on jacob

>>6293446
success breeds jealousy

>>6291859
People ITT are idiots. Complexity theory has been around WAY less time than number theory et al. Then people run into a hard problem and cry MRRRHRHRHH IT'S UNSOLVABLE. No. There are plenty of open problems in the field just because it's only been around a few decades.

>>6287418
you're a retard.

>>6285410
>how dare they make it so anyone not in muh super sekret math club can understand
This is why I hate mathematicians.
Anyway, can somebody tell me what this gradient symbol with no argument means?

>>6284959

So ... does that mean we can stop running evolutionary algorithms to solve fluid mechanics problems?
He probably "just" proved the existence of a solution...

Funny though, this guy gets a million for proving there is a solution. The guy who finds that solution though gets fuck all... apart from the patent and a shitton of resulting revenue, which will probably make him a billionaire.

Go, Science!

>>6293912
What?
<span class="math"> \mathbf{v} \cdot \nabla = \nabla \cdot \mathbf{v} = \mathrm{div}(\mathbf{v})[/spoiler]

>>6293974
thanks
that is some truly horrible notation

>>6294019
Nah, what he wrote is wrong. It's
<span class="math">( ( \mathbf{v} \cdot \nabla ) \mathbf{w} )_j = \sum_i v^i \nabla_i w_j [/spoiler]
i.e. the product between the v-vector and the gradient is a differential operator, namely the change along v.