Terence Tao

He introduced new quantities, kind of like energy, that looked the same at every single scale and turned the problem into a critical one where the nonlinearities actually suddenly looked a lot less scary than they did before.

And then he had to solve, he still had to analyze the singularities of this critical problem.

and that itself was a problem similar to this wave map thing I worked on actually so on the level of difficulty of that so he managed to classify all the similarities of this problem and show how to apply surgery to each of these and through that was able to resolve the Poincare conjecture so

quite a lot of really ambitious steps and like nothing that a large language model today, for example, could.

I mean, at best, I could imagine a model proposing this idea as one of hundreds of different things to try.

But the other 99 would be complete dead ends, but you'd only find out after months of work.

He must have had some sense that this was the right track to pursue because it takes years to get them from A to B. So you've done, like you said, actually, even strictly mathematically, but

I'm a fox, I'm not a hedgehog.

You can modify the problem too.

If there's a specific thing that's blocking you, some bad case keeps showing up for which your tool doesn't work, you can just assume by fiat this bad case doesn't occur.

So you do some magical thinking.

strategically, to see if the rest of the argument goes through.

If there's multiple problems with your approach, then maybe you just give up.

But if this is the only problem, then everything else checks out, then it's still worth fighting.

So yeah, you have to do some forward reconnaissance sometimes.

And that is sometimes productive to assume like, okay, we'll figure it out eventually.

Sometimes actually it's even productive to make mistakes.

So one of the, I mean, there was a project which actually we won some prizes for.

We were four other people.

We were working on this PDE problem.