> In short, it seems to me that while a flood of “big” AI results would be likely to increase the amount of important mathematics that was not properly digested, it would also be likely to increase the amount that was properly digested, which seems like a pretty good bargain.
This seems like the crux of the argument to me, and I agree.
> my worry is not that we would be unable to [digest the mathematical results from the AIs], but rather that the social structures that currently support this digestion process will be destroyed and not adequately replaced.
A valid concern! And one we will all face soon enough, as AI continues to automate parts of jobs that were once manual.
Yup, exactly. The problem looks like this:
(1) OpenAI is merely abusing math problems for their PR stunt. That is, once the PR value dries up, they'll leave.
(2) OpenAI, and any AI companies, can incur serious harms to the social dynamics in the field of mathematics by taking away big prizes away from mathematicians.
(3) The current gen AI is too inefficient -- requires a lot of money to operate -- so it's near impossible for academia to replicate what OpenAI invested in Navier-Stokes.
(4) Also, human experts are still economically much more efficient in searching critical directions, as we saw in the case of Navier-Stokes. The best working model is human-AI collaboration, with AI taking over the grinding part. This is what OpenAI failed to recognize.
Thus, the aggressive campaign from OpenAI is socially harmful -- disrupting a working social system without offering any alternate working sustainable system.
1, 3, and 4 are likely to be resolved IMO. Others will get access to these models, they will get dramatically more efficient quickly, and the AIs will likely pass a point where they don't really need that much human collaboration to solve these problems.
2 is the concern. Even in a world where AIs become all-powerful oracles for math, we still need human mathematicians to ensure we as humans can understand the results, and direct progress toward areas that benefit humans. But this is a new role, very different from the current role of mathematicians. Current academics don't want this role and the upcoming generation of students probably don't either.