it is that this position contains primes. - It's the substitute for the Riemann hypothesis on average, and it turns out that that's what's actually necessary in a lot of these arithmetic applications.
And for a while everything seems kind of chaotic, circling around the origin, but then, when alpha hits 1 over 6, the tail unwinds, But he did it without the generalized Riemann hypothesis .
And for a while everything seems kind of chaotic, circling around the origin, but then, when alpha hits 1 over 6, the tail unwinds, you don't need the Riemann hypothesis .
And for a while everything seems kind of chaotic, circling around the origin, but then, when alpha hits 1 over 6, the tail unwinds, - It's one thing to just assume the Riemann hypothesis , and say, "Oh yeah, you can make some progress." But Vinogradov's like, "No guys,
And the second one is proving those. So for example, the Riemann hypothesis is a great discovery that Riemann made, that, to understand prime numbers, we need to understand the zeros of the Riemman zeta function. Now it's up to one of us to try and prove that his hunch about what this connection says is actually true.
it is that this position contains primes. - Now, the Annals gets a proof of the Riemann Hypothesis every other day, so they're like, okay, surely this isn't gonna work out,
And for a while everything seems kind of chaotic, circling around the origin, but then, when alpha hits 1 over 6, the tail unwinds, They then showed that, if the generalized Riemann hypothesis is true, then the main term grows faster than the error term.
I mean, I think laziness is often thought of as one of the deadly sins, but I don't think it's a sin at all. So I think where the limitations will be is-- for example, even just something like the Riemann hypothesis .
And they're not going to be attempts to solve math-contest problems. They're going to be attacks on the most fundamental and important questions of the day, whether it's the Riemann hypothesis , Navier-Stokes or P versus NP, just to pick a few.
And that is the fundamental key that makes it possible to use Leibniz's vision to unlock the full potential of AI in mathematics. Because when a math AI spits out a proof in Lean of, let's say, the Riemann hypothesis , we're not going to need humans to go through every single line of the proof in painstaking detail, check every single case, and understand the possibly strange and alien logic of the proof just to see if it's correct.
One that gives you pause, maybe? - Well, I mean, in your undergraduate education you learn about the really hard, impossible problems like the Riemann Hypothesis , the Twin-Primes Conjecture. You can make problems arbitrarily difficult.
and because it was solving a problem of more than 50 years old about the behavior of plasma physics. It's crazy constraint. You know, famous problem in mathematics is the Riemann hypothesis .