Transcription
I think what's significant about this moment is that it's the first really clear example of AI solving not just an unsolved mass problem, but a really well-known unsolved mass problem.
This is the first mathematical breakthrough due to an AI. It's, it's been described as the most well-known problem in combinatorial geometry. Uh, so for, for a whole sub field of mathematics, it's like maybe the best known problem there is.
So I remember seeing an initial version of the model output. I sort of didn't really believe it. It took quite a while sort of reading over, trying to figure out roughly what was happening.
I was like, "You cannot be serious." I mean, this, this sounds like too good to be true. And we turned it to a few of the air questions that, you know, many, many people are interested in. And to our surprise, it came back with a solution to one of the most important air questions.
This problem is about points in a plane. It's a completely elementary geometric problem. But the solution involves really deep tools from algebraic number theory. And it was believed that the construction was, uh, was basically best possible. But what our model did was show that this construction could actually be improved by, by quite a bit. Humans were not able to execute this approach; like it was just too delicate. There were too many decisions to make along the way of a proof, and the AI has been able to explore all of these possibilities much more comprehensively, and doing that, it found a path. It found a way to the solution.
Yeah, I, I really couldn't believe it. I, I had trouble sleeping for the first couple of nights. I, I was just really blown away.
Oh, it's very hard to sleep, man. Why it's there to say, uh, you know, like I was expecting AI to do something like this, but I think that my timeline got shortened a lot by this result.
And so what this tells us is that AI is able to make breakthroughs in science and can enable breakthroughs not only in mathematics but in engineering, in physics, in biology, in medicine. This result is showing glimmers of a, a golden era for mathematics.
I think it, this result is a big step up from what we had before, and will, I think it'll be looked back on as a really quite important moment in the history of mathematics.