Accelerating scientific discovery

“There is no doubt that the solution to the unit-distance problem is a milestone in AI mathematics: if a human had written the paper and submitted it to the Annals of Mathematics and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that.”

“The model’s CoT is deeply interesting. It is noteworthy that a significant majority of the thoughts are trying to construct a counterexample to the widely believed upper bound, rather than trying to prove it. This argues that the model has some combination of good intuition, willingness to try approaches considered long-shot by the community, and a predisposition to attempt constructions.… In my opinion this paper demonstrates that current AI models go beyond just helpers to human mathematicians – they are capable of having original ingenious ideas, and then carrying them out to fruition.”

“This is a really impressive piece of work, and I would accept it for any journal without hesitation. I actually briefly worked on this problem and tried to make a counterexample, but failed to make progress… It is definitely an intimidating construction to see through even if you know what is going on, and even harder to go play for yourself.”