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What technological advancements can we expect from solving the millenium problems

Anonymous Tue 09 Feb 15:06:19 2021 No.12685820 View Reply Original Report

Quoted By: >>12685844 >>12685942 >>12686508 >>12689033 >>12690712 >>12691349 >>12691432 >>12691748

So, as we all know there were 7 problems

>Poincare conjecture - solved by Grigori Perelman
So of what use is understanding this problem? can this maybe be used in 3D-Modelling or animations?

>P versus NP - unsolved
The use of this is clearly increasing computational speed

>Hodge conjecture - unsolved
i dont even...

>Riemann hypothesis - unsolved
P R I M E S - obviously cryptography

>Yang-Mills existence and mass gap - unsolved
quantum physics 'n shiet

>Navier-Stokes existence and smoothness - unsolved
This would be YUUUGE for engineering

>Birch and Swinnerton-Dyer conjecture - unsolved
???

So, why are there so many problems in this list that will not contribute to any reallife advancements other than "well that's nice to know"

Anonymous

Anonymous Tue 09 Feb 2021 15:14:24 No.12685844 Report

Quoted By:

>>12685820
We don't know exactly how the solutions would benefit humanity, but it's often the case that the value of maths only becomes clear many decades after the maths was invented.

That's another point, solving some of them may lead to developing new theories, which could be applied to other problems as well.

Anonymous

Anonymous Tue 09 Feb 2021 15:46:35 No.12685942 Report

Quoted By: >>12689023

>>12685820
>The use of this is clearly increasing computational speed
It has nothing to do with computational speed.

Anonymous

Anonymous Tue 09 Feb 2021 15:57:49 No.12685997 Report

Quoted By:

Poincare conjecture and Hodge conjecture both deal with relations of some geometric/topological structure to some algebraic structure which are easier to work with computation wise.

Understanding to what extent the algebraic objects capture the geometric structure and to what extent it is a facsimile of that structure is valuable for understanding computations that you might want to do. The solution of millennium problems isn't meant to be valuable in and of itself, but rather to promote further understanding into topics/fields that have a lot of potential to be valuable.

Anonymous

Anonymous Tue 09 Feb 2021 17:47:51 No.12686508 Report

Quoted By:

>>12685820
poincare applies to building better systems for solving DEs that show up in bio, chem and fin

Anonymous

Anonymous Wed 10 Feb 2021 00:15:22 No.12687858 Report

Quoted By:

None of your theorised uses are actually potential uses.
Cryptography already assumes you cannot break hash functions, hence a bunch of shit about primes and complexity of algorithms.
Yang-mills is inconsequential because physicist use perturbation theory and the experimental results fit like a glove.
Engineers already assume navier stokea equation has solutions, they just use finite difference schemes to solve it for their desired initial conditions.

They are difficult math problems, and their answers will probably involve a lot of middle groud work on theory. Most of these proofs are about building a huge theory, and then they show more general results and the desired conjecture is a special case of some more general theorem that they find, like a corollary.

Anonymous

Anonymous Wed 10 Feb 2021 08:01:55 No.12689023 Report

Quoted By:

>>12685942
this, p vs np is being able to determine the limits of computational efficiency and classify problems based on their most efficient solution in the worst case scenario.

p could equal np but have an exponent that makes p problems intractible and p could not equal np but np might be sub exponential and the problems would be tractable.

Anonymous

Anonymous Wed 10 Feb 2021 08:04:26 No.12689033 Report

Quoted By:

>>12685820
>prove that np = p
>use that to solve all the other problems
>???
>profit

Anonymous

Anonymous Wed 10 Feb 2021 09:59:32 No.12689252 Report

Quoted By:

op you are an enginigger arent you?

Anonymous

Anonymous Wed 10 Feb 2021 19:35:40 No.12690712 Report

Quoted By: >>12690789

>>12685820
Wouldn't P = NP prove existence is deterministic?

Anonymous

Anonymous Wed 10 Feb 2021 19:54:20 No.12690789 Report

Quoted By: >>12691156 >>12691199

>>12690712
No, don't make me post a soi face. P = NP doesn't have any "special meaning", computer scientists treat it like it's some magical barrier separating Bach from normal people, or whatever, but that's simply not true. It doesn't have anything to do with consciousness, or "humanity" or whatever.

P = NP is just a statement about second order logic, it's just saying that there exists expressions in second order logic that cannot be expressed in first order logic with a certain iterative convergence property.

Anonymous

Anonymous Wed 10 Feb 2021 21:37:55 No.12691156 Report

Quoted By: >>12691166

>>12690789
>computer scientists treat it like it's some magical barrier separating Bach from normal people
no they fucking don't lmao. They treat it like it is: an elementary statement with no proof using only elementary means.

Anonymous

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Anonymous Wed 10 Feb 2021 21:42:08 No.12691166 Report

Quoted By:

>>12691156

Anonymous

Anonymous Wed 10 Feb 2021 21:50:12 No.12691199 Report

Quoted By:

>>12690789
>P = NP is just a statement about second order logic
More precisely, ?SO != FOL+LFP. Full second order would give you the polynomial hierarchy. But it's not because it has a purely logical explanation that it has no computational content either. Finite model theory definitely has a computational vibe.

Anonymous

Anonymous Wed 10 Feb 2021 22:30:17 No.12691349 Report

Quoted By:

>>12685820
Do you even /sci bruh? Riemann has been solved and posted to /sci multiple times.

Anonymous

Anonymous Wed 10 Feb 2021 22:58:23 No.12691432 Report

Quoted By:

>>12685820

The point of these problems are not immediate uses, the results may have applications, but these are mainly mathematical problems, not engineering/physics/CS problems.

>The use of this is clearly increasing computational speed
Nope.

>quantum physics 'n shiet
Almost purely of mathematical interest, even most physicists in subfields of subfields don't care.

>This would be YUUUGE for engineering

Engineers don't care, all solutions are numerical and approximate, the millennium problem is almost purely of mathematical interest.

Anonymous

Anonymous Thu 11 Feb 2021 00:34:23 No.12691748 Report

Quoted By:

>>12685820
Clay's institute doesn't respond to emails, otherwise it'll have had been solved now.

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