After Claude Fable disproved the Jacobian conjecture (#1528695) and GPT-5.6 disproved the Dinitz-Garg-Goemans conjecture (#1530401) all in the last week, GPT 5.6 just solved another 6 open Erdos problems.
https://xcancel.com/Qiaoqiao2001/status/2080003441821163958#m
must be so weird to be a mathematician right now... I'm sure not everyone is excited to jump into the AI bandwagon but what choice do you have? Things will likely only accelerate..
How does this affect publications and promotions?
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.
Imagine if you're a unknown, up and coming mathematician and you come up with an actually significant mathematical proof / finding and everyone assumes you used AI? Things are going to be weird...
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.
I'm no math head, but these kind of things are pretty cool!
His prompt was fairly short for the first one in the list:
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