Implications of the millenium Prize Problems

What will the millenium prize problems actually yield when solved? Are they just useful to further our understanding of maths or do they have any other useful applications?

Birch Swinnerton-Dyer conjecture is essentially the bridge between the analytic theory and the algebro-geometric theory of elliptic curves. It's been extremely useful for predicting behaviour in these areas of study, yielding results that would have been otherwise difficult to suggest.

The Riemann hypothesis is the key to understanding the behaviour of primes but as far as I know the more interesting question is the generalized Riemann hypothesis, which gives well, more information about how primes behave.

Essentially anyone working in number theory takes the above two for granted when doing research.

The Hodge conjecture would probably take a semester to explain depending on background

Yang-Mills is the one they threw in so the physicists could be happy

P=NP same deal but for CS majors

Navier-Stokes was put in for the feminists since physics is sexist for being rigid and not fluid enough

I like how this post starts really well and gradually descends to shitposting

It starts as imma shitpost but do so subtly and respectfully, then descends into idk what i'm talking about but i'll shitpost anyway.

Which is the level of quality that we should all strive for.

>What will the millenium prize problems actually yield when solved?

Nothing. Most all math is completely useless in the real world and highly inaccurate. They only do this shit for mental masturbation and grant money.

>this retard actually turned down a million dollars

they seem to be the tools we need to build a bridge linking the intrinsic qualities of the higgs field to the effects of observed gravity in our universe that we label "dark" matter.
>idfk

tahnks for contribootin

If by "useful application" you mean when the problem is solved it immediately lets us do something new and exciting that has an impact on actual lives, then no, none of them has an immediate useful application.

The one that comes closest is P vs NP, and only if it actually turns out that P = NP, and if someone also actually writes down a practically efficient (not just polynomial-time) algorithm for an NP-hard problem. This would change the whole landscape of computation. Most immediately and prominently, it would become practical to break most modern-day encryption.

But nobody really expects P = NP anyway. The problem is unsolved because we don't have good enough tools for proving that hard-seeming problems are actually hard, not because it's plausible that those hard-seeming problems are actually easy.

If it's solved in the non-crazy direction, i.e. if someone finally proves that P != NP, then it's not any more impactful than the other millennium problems. The only people whose life would get exciting are researchers interested in the problem.

>P=NP
>Navier-Stokes

Only these two will have some applications if a positive outcome is achieved, else it will be just be another failed trajectory for math faggots.

erryday an engineer gets a stroke because of navier-strokes
mathfags think that there is no application for navier-stokes

Tomorrow some mathfag proves that the Navier-Stokes equations have solutions in the sense of the millennium problem. It's just an existence theorem, of course, it doesn't give you a nice formula for the solution in terms of the initial conditions; that's too good to be true. How is an engineer's relationship to the Navier-Stokes equations affected by this development?

>if a positive outcome is achieved, else it will be just be another failed trajectory for math faggots.
This is the best part. Especially because P!=NP.

>NS problem
>applications

Not any more than the usual work in pure mathematics. You know it won't tell us anything about turbulence and chaotic flow, right? All the NS problem asks is whether the equations /have/ solutions, and that they exist and are well-defined. Nothing about the nature of the solutions that we don't already know. Besides, the technicalities of the proof, if in the affirmative, will be far beyond any engineer and physicist's understanding -- it will require multiple layers of de-abstracting to make the results in any way useful, besides being able to say "okay, we can keep using these equations."

Also, P almost certainly does not equal NP.

A definitive answer to P=NP will almost certainly have no consequences.

All the proofs so far have, according to the few people who actually understand them, innovative ideas to the point where no longer would matter if the proof is wrong - the theorems that were needed to proved in between took further of understanding of mathematics.
In reality, nearly no one understand them or has read them with care, they're too technical even for most mathematicians - this means we should believe in intellectual honesty if we're going to take their word.

As for applications, generally no. Most mathematics is only done for mathematics itself.

so the higgs field interacting with the higgs field? wtf was i thinking? why did i post this itt? i've got to stop watching bbc documentaries while half asleep. sorry /sci

When the zeros of riemann zeta are proved, a bunch of guys who have a mathematician as a wife will get laid.

Might provide the spark you needed to save your marriage.

If the theorems get proved then that would mean that we can finally use those theorems to prove other shit that could only be proven if, say, the riemann hypothesis is undeniably true.

I don't keep up with this shit but I am sure that by now this has happened with what Perelman proved.

So the application is allowing math PhDs to keep making it rain.

right. if he was truly intelligent, he would have accepted the money and put it to good use, such as animal charities or really anything, even if he didnt personally want anything to do with it.

>Theoretical science has no real world applications

Half of those aren't even MPP. Just fuck off if you're going to try to wave your dick with unrelated shit

nope, you're not right. you might as well say that the trolley problem has a definitive correct answer

If your gonna b8, do it well. So posting this "Mathematics is useless XDXDXD" shit. It isn't funny, nor true. It's just blatant and idiotic shitposting.

Exactly my thoughts.

hodge is easy to explain if you're not a complete autist.

There's a space CP^n where a point is a n-tuple of complex numbers. We then look at smooth surfaces/curves in that space, they're smooth complex algebraic varieties, basically solutions of polynomial equations. Now if we only consider such objects we can then look at special drawings we can make on them. These drawings are called algebraic cycles. They also correspond to polynomial equations, kinda the complex analogues of conic sections. We also consider topological cycles which are loops that can be drawn using simple elements called simplexes. The Hodge conjecture then tells us that on any such special manifold, any topological cycle can be expressed as rational linear combinations of algebraic cycles. It's also important to note that these algebraic cycles are special in the sense that they can also represent a special vector field on the manifold.

It is useless to the majority of the working world. Incredibly useful in academia, but knowing calc or higher math will not help you be a better janitor or salesman.

An obvious example of this is how convoluted and ridiculous most word problems have to make ordinary situations sound to shoehorn in the need to use specific equations.

> traveling salesman problem doesn't help salesmen
Also
>
An obvious example of this is how convoluted and ridiculous most word problems have to make ordinary situations sound to shoehorn in the need to use specific equations.
How's middle school?

Useless to the majority of the world =/= Completely useless.

Yeah math is incredibly useful in academia. That contradicts your claim that it's inaccurate, since if it were, nobody would be using it in the first place. I don't think engineers would want to fuck with an inaccurate science, since that would not only cost them money, but possibly injure or even kill a few individuals. Likewise, physicists wouldn't fuck with it since it wouldn't produce a consistent theory due to its inaccuracies. Yet, both these groups use math on a regular basis. Gee, I wonder why?

Also, most real life situations don't involve a knowledge. A salesman could benefit from traveling salesman problem. A janitor most likely doesn't have any sort of education beyond high school and even so, their job is pretty routine and straightforward (just clean shit), so I guess that's true though.

Furthermore, most word problems aren't even that convoluted. If you don't have ADHD and/or autism (which I doubt), it literally gives you all the materials you need to solve the problem inside the wording. The point of the word problem isn't to be 100% realistic, it's to teach you a mathematical concept. Who ares how realistic it is? The point of the problem is to understand the nature of the problem and solve it in a manner that gives the correct answer (i.e. use the right equations and properties). It could fucking involve aliens and shit, I don't care. Just as long as it gets the mathematical concept it's trying to portray to the person answering the question correctly, I'm fine.

Why do all the high schoolers here have to be so contrarian and mentally challenged that they have to be vocal when they clearly don't know what they're talking about?

Do you have any idea what you're talking about or do you just go in threads to put in filler nonsense?

>A salesman could benefit from traveling salesman problem.
janitors probably benefit from it more than anyone