Which millennium problem you guys think it'll be solved next?

Which millennium problem you guys think it'll be solved next?

Poincaré conjecture

naive strokes was solved by that kazakh guy

Poincaré conjecture

*Insert edgy reasoning by a freshman compsi claiming he had already solved P vs NP*

I just wanna see the meltdown after one is shown to be undecidable.

1. Take the polynomial algorithm that checks if a solution is correct.
2. Reverse it.
3. It has a complexity of [math]\frac1{P(n)} \,=\, o(1)[/math] and is therefore polynomial.

semi-decidable would be more annoying

P!=NP is a long time away

have you decided what you're going to do with the money yet?

is p and np even provable

Riemann Hypothesis.

How about the navier-stokes? I believe people from all over the world are working on it and doing some progress.

He failed IIRC.

Riemann Hypothesis. In hindsight of how the Poincaré conjecture was proven, it all happened because a sequence of autists used their autism to discover more and more until the final autist completed the puzzle.

Well, complex analysis autists have been hard at work for a long time now. The kind of shit we can prove is now absolutely ridiculous. And I bet you that the final autist looking to complete the puzzle is hard at work as we speak typing into latex.

...

>In hindsight of how , it all happened because a sequence of autists used their autism to discover more and more until the final autist completed the puzzle.

Not really. Most mathematicians are not autistic. There are at all times a handful of autistic mathematicians in the world. But when two or more autists start working on the same problem they tend to strike gold.

Most mathematicians are non-autists who never really discover new stuff, they just apply techniques developed by autists to prove some useless lemma and get a publication.

A college degree.

not in any meaningful sense, no

the "easiest" way to come to a conclusion would be to show that there is a problem in the NP class that (for some reason) can NEVER be solved in polynomial time.

this not tell us anything about the rest of the problems, and would be extremely difficult to prove by itself

>this not tell us anything about the rest of the problems
It does if the problem is NP complete.

proving a single NP complete problem cannot have a polynomial time solution tells us nothing about the rest of the NP complete problems

you appear to be confused about what NP-Complete is.

All NP problems are reducible to a NP-Complete problem in polytime
Suppose a NP-Complete problem C1 provably has no polytime solution
Then for contradiction suppose another NP-Complete problem C2 does.
Reduce C2 to C1 in polytime
C1 now has a polytime solution

ah, yeah, i mixed up NP-Complete with NP-Hard

N = 1
∴ P = NP
Q.E.D.
Do I win?

all of them at once through post-anabelian froeboid geometrics

This is literally at the level of "why is 6 afraid of 7". Stop repeating it.