alt Hacker NewsUnlike the unit distance problem, the impressive thing here is that it is a proof rather than a counter-example.
However, it seems the proof is extremely concise so it seems that it is exploiting a clever trick that somehow all the experts missed.
So not to dunk on this amazing result (or move the goal post), but it seems now the only achievement that AI hasn't managed in mathematics is presenting an autonomous "theory-building" proof of an open conjecture. That is a proof that requires creating a substantial new theory (developed say in at least 30+ pages) to crack an open problem.
Replies
For comedy’s sake, I asked ChatGPT 5.5 about the significance of the problem and the chance that 5.6 would solve it with a three page solution. It said close to zero.
I invited it to search the internet and it remains extremely sceptical.
> However, it seems the proof is extremely concise so it seems that it is exploiting a clever trick that somehow all the experts missed.
Why is that a "however"? My reading is that it found a genuinely new solution that is both elegant and previously missed.
Seems like exactly the kind of result a human mathematician would aspire to.
I wonder if in each case they had parallel sessions, one trying to prove, one trying to find a counterexample
> seems that it is exploiting a clever trick that somehow all the experts missed.
Exactly, "clever". Isn't that the whole point?
It is very concise, and reads precisely as you suggest: to exploit properties already discovered and therefore combined in a novel way.
I'm just delighted by the prose. It reads like an old paper. The ones that were just straightforward theorems with proofs that do exactly what they say.