AlphaProof

“Tim Gowers, who was one of our judges and is also a fields medalist. Tried this question for a couple hours and he couldn't find the construction for function that had this property”

“And to be honest with you know, like kind of we, at the moment we can't rival at all with someone like Terry Tao. We, I think we demonstrated that what we've demonstrated is that we can learn general mathematics almost from scratch and arrive at kind of an imp…”

“Some of the sort of tech we developed here of like, you know, like scaling RL and like figuring out how to spend a lot of inference time compute stuff like this feels like it's Quite generally applicable to many other problems.”

“The way alpha proof currency operates there is that it discovers its own proofs, and when they are valid, it learns from them and develop its own style which has been commented upon as looking, yeah, quite, quite alien.”

“Maybe the main thing that Alphaproof doesn't do is theory building. It doesn't invent its own theories.”

“So the IMO problems have come in four categories. So there's algebra number theory, combinatrix, and geometry. The two that it's strongest at are algebra and number theory. It's relatively weaker at combinatrix, although it can do quite good at some IMO combin…”

“With more supervised data, we can avoid the exploration problem, and we could translate all the proofs that are known to man, and that certainly would make the agent much better, and that would save us years of compute for sure.”

“Alphaproof had this really amazing results of solving four of the six problems this year.”

“The advantage of that is that once kind of the proof is complete then you know, the machine would give you a signal back to say, yes, your proof is correct or not. And so we could search for kind of correct proofs. Once we find a correct proof, we can learn fr…”

“One of the ways in which it navigates this massive search space is via an idea that we came up with, which we call test time RL. So this is an idea where, like, let's say you're confronted with a problem that you don't know how to solve. And you know, you can …”