Terence Tao

Yeah, you got the right answer, you got the wrong answer.

It's a very clear signal.

But a long-form proof either has to be formal, and then the lean can give it thumbs up, thumbs down.

or it's informal, but then you need a human to grade it.

And if you're trying to do billions of reinforcement learning runs, you can't hire enough humans to grade those.

I mean, it's already hard enough for the last language learners to do reinforcement learning on just the regular text that people get.

But now if you hire people and not just give thumbs up, thumbs down, but actually check the output mathematically, yeah, that's too expensive.

That's a good question.

I think the nature of what mathematicians do over time has changed a lot.

You know, so a thousand years ago, mathematicians had to compute the date of Easter, and those really complicated calculations, you know, but it's all automated, been automated for centuries.

We don't need that anymore.

They used to do spherical trigonometry to navigate how to get from the old world to the new.

Very complicated calculations.

Again, we'd been automated.

Even a lot of undergraduate mathematics, even before AI, like Wolfram Alpha, for example, it's not a language model, but it can solve a lot of undergraduate level math tasks.

So on the computational side, verifying routine things like having a problem and say, here's a problem in partial differential equations.

Could you solve it using any of the 20 standard techniques?

And the AI will say, yes, I've tried all 20.

I hear that 100 different permutations and here's my results.

And that type of thing, I think it will work very well.