Comment by gste
8 hours ago
> Using AI to find and highlight new principles, methods, or insights, rather than merely new proofs.
I would have assumed that, by producing new proofs, the AI has either validated existing principles, or discovered new ones? Isn't that worth studying?
Are mathematicians complaining that reviewing AI's proofs is not as fun as writing your own? Try being a programmer... welcome to our world!
If AI lacks imagination and is not discovering new principles, then it's doing us a favour: it's crossing out the problems that don't need new principles. So the problems/conjectures that are still left are the more interesting ones.
I have done both scientific research and software development, they are not the same world. For a start, when you write a program you have a specific goal. When you ask a scientific question, you often don't.
Absolutely not. New proofs aren't the same thing as new proof techniques, AI is not generating new techniques (yet), and while the existence of more mechanical proofs is interesting those same problems if left to human mathematicians would have been much more likely to actually generate new techniques. Much like how tech has a "juniors" problem we're pushing on the future (no reason to hire juniors, so where are tomorrow's staff engineers going to come from), OpenAI's approach generated a "questions" problem where math and AI could happily coexist if we designed that correctly, but instead nobody's going to be generating or working on the right questions anymore.
> AI is not generating new techniques
Source? I assume that many of the approaches embedded in this proof dump will eventually be distilled and generalized into new techniques. That's how proof techniques tend to come about anyway (before AI): human mathematicians do something novel and unexpected to solve a particular problem, then efforts are made to understand how the "trick" works.
The point is that so far the AI is not doing a good job at explaining the "trick", so we (humans) have to do it. And the way these results are published at the moment (that is, dumping a load of proofs with badly written explanations) is not cooperative to enable this distillation (for example, presenting results at conferences and engaging with mathematicians). I recall Tao working through the disproof of the Jacobian conjecture, stating some steps as "miracles" for lack of better terms. If a human solves a problem in an unexpected way, at least there is some reason why they chose this path, which can help in understanding. This is not available to the same extent with AI generated proofs.
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