Scott Aaronson on the Impact of AI on Science and Mathematics

Well, I mean, I should start by saying I'm not an expert on differential equations or on the Navier-Stokes problem, but I can certainly tell you in general about these millennium problems.

There's another one of them that I am an expert on, just not this one, not the one that was solved.

So these are seven problems that were put forward by something called the Clay Math Institute, I think the year 2000.

And they were inspired by a mathematician named David Hilbert, who in 1900 had put forward 23 problems that he felt could shape the course of math in the 20th century.

And this was enormously influential.

Hilbert's list of problems.

Some of them have been solved.

Some of them still haven't been solved.

Some of them were kind of vague, and it's not even clear what counts as a solution, and yet they were still very influential.

And so this Clay Institute picked seven problems, each of which has a million-dollar prize.

I should say, no one who would seriously work on any of these problems is doing it for the money.

This is one of the hardest million dollars that you could possibly get.

But the problems are, well, there's the P versus NP problem, which is the one that I know the most about.

Then there's the Riemann hypothesis.

That's the only one of the seven that was recycled from Hilbert's problems and still hasn't been solved.

And then there was a central question in topology called the Poincare conjecture.

That was the first one to be solved.

That was solved only a few years after the Clay Institute announced these things.

Right.

by a guy named Grisha Perlman, who then very, very interestingly refused the prize.

Also refused the Fields Medal because he just no longer wants to be part of the mathematical community.

As I said, people are not doing this for the money.

And now we have what looks like the second clay problem to have been solved.

And as I think No one was expecting, you know, when these problems were proposed, you know, were listed 25 years ago, this solution came largely from AI.

Right.