Terence Tao

Yeah, this idea of building up cumulatively from partial progress is what's still not quite there yet.

Yeah, you run a new session and it's forgotten what it just did.

It has no new skills to attach to build on related problems.

Maybe what you just did is part of 0.001% of the training data for the next generation.

So maybe eventually some of it gets absorbed.

Yeah, we don't know.

I mean, some problems have been basically solved by pure brute force.

A four-color theorem is a famous example.

We have still not found a conceptually elegant proof of this theorem.

It basically...

And maybe we never will.

I mean, some problems may only be solvable by just splitting into some enormous number of cases and doing a brute force, an insightful computer analysis on each case.

I mean, part of the reason we prize problems like the Rune hypothesis is that we're pretty sure that something amazing has to, a new type of mathematics has to be created or a new connection between two previously unconnected areas of mathematics has to be created.

discovered to make this work.

We don't even know what the shape of the solution is, but it doesn't feel like a problem that will be solved just by exhaustively checking cases or something.

I mean, it could be false, actually.

We could actually, okay, there is an unlikely scenario that the hypothesis is false, and you can just compute, oh, here's a zero off the line, and a massive computer calculation verifies it.

That would be very disappointing.

I don't know.

I do feel that fully autonomous one-shot approaches are not the right approach for these problems.