Terence Tao

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.

Again, actually this blow-up regularity type problem.

And it was considered very hard.

Jean Bourguin, who was another field specialist who worked on a special case of this, but he could not solve the general case.

And we worked on this problem for two months, and we thought we solved it.

We had this cute argument that if everything fit, we were excited.

We were planning celebrationary to all get together and have champagne or something.

And we started writing it up.