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I’m a mathematician, but work in an applied field – AI, actually – that has not yet been impacted by…
Kelsen was certainly right about U.S. law schools in the 1940s and for a couple of decades thereafter. By the…
I don’t know about antisemitism. I think it is more generally a kind of contempt for European exiles (most of…
Having attended a few talks by leading mathematicians working on fluid dynamics after the OpenAI solution of the NS problem…
I had not looked at either of those sources, thanks for the pointers. I take it you’re suggesting that anti-semitism…
I’m no Fuller aficionado, but the role he played in Harvard’s refusal to hire Kelsen seems to be wildly overstated…
Obviously what’s changed in the meantime is how much this has become a buyer’s market (and thus, an arms race…
Reader Blake Myers calls to my attention this story about the mathematical proofs released by OpenAI. Dr. Myers kindly compiled what seemed to him the most interesting or important results here. The total collection of papers is here. Readers knowledgeable about math are welcome to comment on these, how they will affect mathematics, etc.
Having attended a few talks by leading mathematicians working on fluid dynamics after the OpenAI solution of the NS problem came out, I feel the current mood in that corner of math is *roughly* as if an alien artifact has been discovered, one which clearly does something remarkable (the Lean formalization adds a lot of credence to the correctness) but we have little understanding of how it works, and so the task the mathematicians in that field have set themselves right now is to transpose the proof into the kinds of ideas that humans have been familiar with. (At least in the NS case, the broad proof strategy was generated by a non-AI-assisted human, Martinez-Zoroa.)
This is still highly nontrivial work given that the proof is subtle and complex and the AI hasn’t written the proof in a clearly understandable manner. Unsurprisingly, this task of “humanizing” the proof is itself heavily AI-assisted.
Based on this, and given the new deluge of proofs, I suspect the future of much math for the foreseeable future will be like reverse engineering alien artifacts. It’s full employment for humans for now, as you need people immersed in these fields to even begin to understand these proofs.
While I’m sure many mathematicians are demoralized, I also get the sense that mathematicians are in good part genuinely excited. There’s a step change in the amount of mathematical knowledge available and that’s an immense thing.
I’m a mathematician, but work in an applied field – AI, actually – that has not yet been impacted by this work.
I’m worried. I’m not really worried for the field as a form of scholarship. This obviously represents a radical new way to do math, but we’ve adapted to radical new kinds of doing math before. If anything, as a mathematician my reaction is to be excited about what this makes possible. What I worry about, a *lot*, is the *economic* implications. Is society still going to be willing to pay people like me to do what we do? The answer is going to depend on several factors, of which the most important is where AI intelligence ends up topping out. Right now AI proofs are horribly written and they can’t really come up with their own questions. I suspect the former problem is almost certainly solvable if the AI companies care to solve it. I have no idea about the second question. I can imagine a near-term future where AI completely displaces humans from mathematics and I need to find a new job. I can also imagine a future where AI is a wonderful new tool and the Jevons paradox means that we end up with *more* mathematicians because there’s so much new math to do.
In the very-short-term, the field needs to sort out new norms around this. For example, if I prompt Claude to prove a theorem, can I publish that under my own name? I think we have to decide that I can, because if not, most mathematicians won’t be able to take advantage of this tool. But if Claude proves the theorem, how much credit should I get for asking the question? The whole system around academic publication is already broken, but AI is going to make the problems even worse.
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