Terence Tao

You can represent all these things as trees, and there's always algorithm to match one tree to another tree.

So it's actually doable to figure out if something is...

a real number or a natural number.

Yeah, every object sort of comes with a history of where it came from and you can kind of trace it.

Oh, I see.

Yeah, so it's designed for reliability.

So, modern AIs are not used in, it's a disjoint technology.

People are beginning to use AIs on top of Lean.

So, when a mathematician tries to program a proof in Lean, often there's a step, okay, now I want to use the fundamental calculus, say, okay, to do the next step.

So, the Lean developers have built this massive project called MethLib.

a collection of tens of thousands of useful facts about mathematical objects.

And somewhere in there is the fundamental theorem of calculus, but you need to find it.

So a lot of the bottleneck now is actually lemma search.

There's a tool that you know is in there somewhere.

and you need to find it.

And so you can, there are various search engines specialized for Mathlib that you can do.

But there's now these large language models that you can say, I need the fundamental calculus at this point.

And I've said, okay, for example, when I code, I have GitHub Copilot installed as a plugin to my IDE.

And it scans my text and it sees what I need.

It says, you know, I might even type, okay, now I need to use the fundamental calculus, okay.