Terence Tao

And we had previous software tools that can work at scale, but very narrow.

So we have to figure out how to use... I mean, so Tim Gower, like you mentioned, he actually foresaw, like in 2000, he was envisioning what mathematics would look like in actually two and a half decades.

And he wrote in his article, like a hypothetical conversation between

a mathematical assistant of the future and himself, you know, he's trying to solve a problem and they would have a conversation.

Sometimes the human would propose an idea and the AI would evaluate it.

And sometimes the AI would propose an idea and sometimes a competition was required and AI would just go and say, okay, I've checked the 100 cases needed here.

Or the first, you said this is true for all N, I've checked N up to 100 and it looks good so far.

Or hang on, there's a problem at N equals 46.

And so just a free-form conversation where you don't know in advance where things are going to go, but just based on, I think ideas are good to propose on both sides, calculations are good to propose on both sides.

I've had conversations with AI where I say, okay, we're going to collaborate to solve this math problem.

And it's a problem that I already know the solution to.

So I try to prompt it.

Okay, so here's the problem.

I suggest using this tool.

And it'll find this lovely argument using a completely different tool, which eventually goes into the weeds and say, no, no, no, try using this.

Okay.

And it might start using this and then it'll go back to the tool that it wanted to do before.

And you have to keep railroading it onto the path you want.

And I could eventually force it.

to give the proof I wanted.