Would that be a bad thing?

While top AI labs no longer focus on chess, the community build way better chess engines.

Stockfish is probably stronger, than everything the top labs build.

Wouldn't we expect the same thing for math? That slowly the broader math community would engineer a harness/program... That will surpass the current labs, and be a community ran project

Yeah its certainly true now that Stockfish is much stronger than alphazero, but it's probably also true that had Deepmind spent another few years working on alphazero it would be enormously stronger than either.

In the case of chess this seems fine, there isn't much value to society in creating an AI capable of beating top humans with a 4 pawn handicap rather than a 2 pawn one, but for maths where there are actual applications it is more complicated.

But arguably - it's better for chess community that the best engines are opensource than having superior GoogleChessBot.

They aren't trying to 'solve' chess, go, or mathematical proofs as an end in themselves, but mainly in order to learn more about how to build better systems overall. The goal of AlphaZero was ultimately as a stepping stone towards AGI, and it's the same with LLMs.

The assumption being that 1. these things are all stepping stones, not diversions 2. that ai labs have a singular goal of producing agi

It's not an assumption, many of the people behind these projects explicitly say this what they are doing and why.

That’s still an assumption. Since when do you uncritically believe what people are saying without taking into account the different external drivers on those people.

You can believe they believe they are telling the truth or that they have good intentions while still being skeptical of the effective trajectory.