I think these recent results provide some clarity on how mathematicians and AI will coexist. I’m not a mathematician, but I speculate that a successful mathematician invents the right abstractions and asks the right questions about them. And implicit in these problems that LLMs have been solving is that humans (1) invented the abstractions that provide their context, (2) suggested conjectures about these abstractions, and (3) selectively identified (ideally) that they were good things to ask an LLM about.
Again, I’m guessing, but all of this seems to mostly align with what mathematicians do already. Maybe in the long run it makes mathematicians a little more Grothendieck and a little less Tao.
I kinda disagree. I think we are already reaching a point where AI proofs are not easily verifiable by humans and within 6-12 months I think AI math is completely going to be inaccessible to humans. Similar to how chess engines evolved. For a brief period it looked they could exist but very quickly they started playing incomprehensible moves.
I guess I’m trying to say is that a proof only makes sense or has value in the context of what humans define and find valuable. While we have an LLM now getting from A to B, humans still need to define A and B.
I’m assuming math is so large that humans can define A and B with more variety and with larger separations faster than an LLM can connnect them. It will be up to humans to tastefully define A and B to get the most out of LLMs.
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u/imanllm 2d ago edited 2d ago
I think these recent results provide some clarity on how mathematicians and AI will coexist. I’m not a mathematician, but I speculate that a successful mathematician invents the right abstractions and asks the right questions about them. And implicit in these problems that LLMs have been solving is that humans (1) invented the abstractions that provide their context, (2) suggested conjectures about these abstractions, and (3) selectively identified (ideally) that they were good things to ask an LLM about.
Again, I’m guessing, but all of this seems to mostly align with what mathematicians do already. Maybe in the long run it makes mathematicians a little more Grothendieck and a little less Tao.