/Grothenfla/will-the-riemann-hypothesis-be-solv-ypNQz5hEgI
Interesting that it's 40% by 2030 but only 50% by 2035. In other words, conditional on it not happening in the next 3.5y, only 10% chance it happens in the following 5y? I can't say that's wrong, but it's interesting. If I was one of these "AI to the moon, graph only goes up" people I would probably think it's wrong.

@pietrokc it suggests that people are putting weight on foom-like things happening in maths. That thinking essentially collapses to a dichotomy: either we're in the fast world or the slow world

it's fairly reductive since we don't know how much effort is required to produce the first valid proof of RH

could still be in the "fast world" and have to wait until 2040+

I think also the dichotomy falls apart in other ways. No all math is equal. You might get superintelligence in certain jagged aspects of mathematics but not in others. But until you do the empirical verification, it's difficult to forecast what we'll get from the current era of RLVR math runs.

My guess is that there's roughly a 40% chance that the capability of producing a valid RH proof gets enclosed by "GPT-6 / Fable-5" class math models. If there are race dynamics then that weights the likelihood of the first valid proof of RH emerging early within this model generation. Hence a surprisingly high chance of a valid proof emerging in 2026.

@0xseraphim I'm curious where you get the 40%.

You're giving this 40% now, but like, they won't stop coming out with new model generations. When GPT-6 fails to solve RH, will you say 40% that GPT-7 solves it, and so on? With a new generation every 2-3y, that would amount to a better than 1 - (0.6)^4 = 87% chance it gets it by 2035. And conditional on not getting it by 2030, a 64% chance it solves RH by 2035.

@pietrokc no I don't think so. If we're in 2030 and it's still not solved then my probability for this "occurring soon" would start to drop off rapidly. I don't consider those probabilities to be independent as your formula implies. I don't think you can just multiply them together like that in the real world.

@Simon74fe the race to the riemann

@Simon74fe Note that this approach is fundamentally powerless to prove RH. The best it can do is show that 100% of zeroes are on the critical line. However, RH means ALL the zeroes are on the critical line. (Since there are countably many zeroes, you could have a finite or even infinite but sparse set be off the line, and still the fraction on the line be 100%. Much like the fraction of integers that are not perfect squares is 100%.)

@pietrokc for sure. But this is just one approach. It doesn't tell you much about future approaches

Noam Brown (@polynoamial) on X

Noam Brown (@polynoamial) on X

And yes we did try other major problems without success. Sadly no Millennium Prize problems (yet). But also, we didn’t spend a lot on each problem. It’s possible to push test-time compute much further.

This is another like the alien spaceship question, where I'm happy to lose my mana if I'm wrong because it'd rock if it got solved.

Satisfiability solver, theorem prover, or other solver of this sort presumably doesn't count unless it's substantially AI.

https://x.com/dmdohan/status/1870176374625054880

Does the AI-generated proof have to be the first-ever correct proof, or would this still resolve positively if humans had previously settled RH and the AI proof came later?

@WilliamDAlessandro Implicit in the title is that the AI has to be the first.