Tyler Cosgrove

And then we theorized that the high bound, upper bound scales with n to the four thirds.

And then so Erdos, the original conjecture that he thought that the upper bound is still going to be less than n to the 1 plus o of 1.

So this means o of 1, it's like as n scales to infinity, right?

So o of 1 basically scales to 0.

It goes to 0 as n goes to infinity.

Basically, OpenAI figured out that this is not true, and that there actually are some n's for which this kind of max number of pairs is greater than the original Erdos conjecture.

So for infinitely many n, this is not for every single n, so it's not like five points or whatever, but there are infinitely many n's for which this is true, that it's greater than n to the one plus some constant.

Okay, so that was basically the big thing, right?

This is like, you know, a decades-old problem, right?

This is an incredible thing.

Terence Tao is like, wow, this is incredible.

But yeah, that's basically the overview of the problem.

But yeah, it's very exciting because this is not like a math model.

This is just an internal model, general reasoning.

Yes, I think you could say that.

And then I think it's interesting because from public perception, it seems like this didn't take that many tokens.

This was not millions of dollars of inference time.

It was maybe something like hundreds to thousands of dollars of inference computing.

Yeah, this is not just taking some solution to a different Erdos problem and just like spamming it on all 1,200 of the problems and oh, one of them works.

This is like kind of a new novel idea.