Do you think we will see the Riemann hypothesis solved before 2100?

I think it is independent of ZFC

I think it doesn't really matter and we should spend our times on more productive stuff

of course good conjectures like this matter, even if you dont know if its true or false, you can work with it and see what follows, lots of other theorems have been proven this way

i saw a paper in the arxiv the other day where a result was previously known if the generalized riemann hypothesis was true, and they published a proof of this result no longer relying on this fact

another major theorem was first shown to be true if GRH was true, and then shown to be true if GRH was false, and so the theorem had to be true

Yeah, I did it a couple of days ago, just working on the paper senpai, gimme a month.

>another major theorem was shown to be true if the GRH was true, and true if it was false
link? this sounds like a pretty funny incident

It was solved in 2006.25

pic from ireland and rosen's classical intro to number theory

h(D) is the class number of Q(sqrt(-d))

>another major theorem was first shown to be true if GRH was true, and then shown to be true if GRH was false, and so the theorem had to be true
this inference is invalid in intuitionistic maths right? because you cannot assume GRH v ~GRH is a theorem from which to do disjunction elimination.

so is there a theorem that GRH v ~GRH for intuitionist mathematicians?

Nobody besides people working on type theory/category theory/automatic theorem provers cares about intuitionistic maths.

The Riemann zeta function is even used on fields of quantum physics, eg, all assuming the Riemann hypothesis is true, so I don't understand why you say the hypothesis doesn't matter.

What would happen if someone proved that any proof of the Riemann Hypothesis could only apply over a finite range?

That is, the best it will ever be able to say is that any zero with imaginary part less than some upper bound, must have real part 1/2.

i.e. It gets proven that it's impossible to extend that upper bound to infinity, the best you can do is improve the proof to some larger, finite, upper bound.

That wouldn't imply that not all zeroes lie in the critical line, but it'd be a good indicator that the RH holds. It'd tell us much more about the proof technique used than the problem itself.

Just imagine if you did the same thing for the number of primes.

>That wouldn't imply that not all zeroes lie in the critical line
Yes, but it would mean you could never prove it.

Everything that relies on the Riemann Hypothesis would forever have an asterisk next to it.

>Yes, but it would mean you could never prove it.
No it wouldn't.

Being restricted to a finite upper bound doesn't mean anything if your finite upper bound can be arbitrarily large.

If there exists a proof that Im(z) < N -> RH for every N, that's good enough.

No, I'm saying you prove that ANY PROOF must have a fixed upper bound.

Proving you can make the upper bound arbitrarily large would itself be a proof... and therefore have a fixed upper bound to which it can apply.

This doesn't make any sense

if N is the "bound" for proofs I can make a new proof that's just N and manually checks (via computer obviously) up to N+1

Yes, and then your new proof would have an upper bound of N+1.

It would say nothing for N+2, N+3, etc

Manually incrementing doesn't magically transform into a complete proof.
Maybe the confusion is with my use of "fixed". I meant fixed for that specific proof. Not as an absolute across all proofs.

I believe that I already know how to solve it. Just have to wait for next year to take complex analysis to know how to put my prove into words.

That's rude.

I'm more interested in the analytic solution of the Navier-Stokes equations and N vs NP.

>wait for next year to take complex analysis to know how to put my prove into words.

kek

I'd laugh if he was right and was sitting on the solution this whole time.

It's already been proved numerous times. The problem is that the jews will assassinate anyone who proves it before their work can be released to the public.

Why does the female have a penis?

if not for you, I wouldn't have noticed that

Fucking finally someone noticed. I've been casting this b8 here for a week and you're the first to reply. Good job.

what's unusual about that? have you never seen a feminine penis?

Nah they just assassinate US presidents who try and undermine their control. Or could solving the Riemann hypotheses give rise to a special anti-Jew weapon?

If I were laid to sleep for five hundred years, and I were resurrected those same five hundred years later by a future race, who had advanced, my first question to them would be, "Has the Riemann Hypothesis been solved?"

>What's your opinion?
In my opinion, you're a clickbait shill.

Everyone noticed, we just didn't care.
>grill with peeenuus XDDDDD