I hope this isn't overlapping with other discussions that have been going on in MathOverflow or in the broader community. As a young researcher starting to navigate the seemingly in-crisis publication world, I'm very curious about how the community is going to adapt (or not) to the fast-paced advances of AI.
Here are the questions:
This comes from the understanding that math is a cumulative discipline, and we may care about the result regardless of who or what produced it. Still, a world in which AI one-shots coexists with works produced by humans (or mainly produced by them) seems extremely unfair.
Implicit in this question is a personal bias that sees human craft as more valuable to the community and the individual than whatever an LLM generates. Obviously, this point makes no sense if the majority of the community is goal-oriented rather than goal-human-oriented. In any case, if we pay humans to be mathematicians, we want to evaluate them for their human labor, not their copy-paste-interpret of someone else's labor (though one can argue that "interpreting" is still a human activity).
This is also assuming that in the near future, LLMs do not become exponentially better than mathematicians at solving problems relevant to mathematicians, but will become extremely good at solving problems that the overall mathematical community can solve, but perhaps cannot do because of the way problems and skills are distributed among individuals of the community. I feel that in a world where LLMs become much better than mathematicians at solving any problem, most of the questions posted here become almost irrelevant, as there would be bigger questions to solve.
I took a slightly arbitrary definition in my previous point, since one could argue that one obtained the one-shot after providing the AI with some intuition on how to solve the problem. Still, there's much more to the mathematical activity than having the intuition.
Just for comparison's sake, I would not describe the following situation as an AI one-shot: a mathematician builds most of a text, but somehow gets stuck with a few lemmas that seem to have room to improve, and then uses LLM's to expand these lemmas. Still, there are many intermediary situations between the last paragraph and this, and it's unclear where to draw a line.
From what I heard, either a counterexample to the Jacobian conjecture or the Erdos problem would have been publishable in top journals a few years ago. What if someone uses an LLM to solve a big problem, but does not acknowledge the LLM? In this scenario, this person would potentially be cheating their way towards a better journal. Conversely, we have the most optimistic situation: a human works on a problem, finds a sophisticated counterexample by themselves, doesn't acknowledge an LLM, and, a posteriori, everyone thinks they used LLMs in their paper. I get the feeling this may be harder to implement. I know that recently, thanks to EU policies, AI companies are forced to include watermarks in their AI-generated texts. Still, there are no guarantees these watermarks will hold after thorough rewriting.
This question is a bit speculative: suppose AI reaches the point where talented humans who use it tastefully consistently produce better results than a very talented human who doesn't or can't access AI. Even if this is not the case, everything points to the person with AI assistance being able to publish much faster. Is it good for the community to essentially lose these mathematicians?
One can argue that if one does not want to adapt willingly, it is the individual's fault for not adapting. I'm more concerned with the situation where mathematicians can't have access to this tool.
Coming from a "third-world country," I know institutions think very carefully about how they spend their money, with things like "should we pay for MathSciNet?" sparking long discussions about where the money should go. Is this another economic burden institutions will have to face to be competitive? This is probably not a problem in the US, where AI providers can potentially negotiate with wealthy institutions for licenses and settle on a "standard price." Whatever this settled price may be, it will be almost impossible for most of the rest of the world to pay.
I apologize for the long thread. I'm happy to read your thoughts on these issues.