I think everyone is struggling to figure out how to reorganize academia (and everything, really) in the brave new world of AI.

My guess is ai-generated contributions will in general not be seen as very valuable for promotion, unless the prompting was particularly inventive, or the human added a crucial contribution in the loop.

But if that happens, then prompters will be tempted to hide the fact that they used AI.... so there will be an arms race between the vibers and ai-detection tools.

As for publication, the whole system is broken to begin with. There's no reason that journals should be capacity limited the way they used to be, when the amount of paper and print literally constrained how much could be published. AI-generated proofs should still be published, since they add to our knowledge-base, but whether they can get published in journals depends I guess on what people view the purpose of journal publication to be. Right now, it feels a lot like journal publication is a prestige-signal / status-good more than anything related to actual knowledge dissemination.

Currently these high profile math proofs focus on disproving and other proofs where the solution can be automatically verified.

I suspect that we will reach a point where there are lots of AI proofs that cannot be verified in an automated way. At that point there will be lots of bachelorthesises and promotions be written where the hard part is following what the AI wrote.

That's my guess at least. Can't see into the future either.