Comment by hansvm
8 hours ago
> solve open problems without producing insightful new methods
> sub-O(nlogn) proof disproves that
How? Re-iterating, creating and understanding new proof techniques is the point of most of modern mathematics. Your statement is that proving a particular result is evidence of AI creating and understanding new proof techniques. I don't see how that follows, and I'm inclined to believe Tao is right for now.
And yes, results matter too, but if we stop at our current body of techniques and strip-mine results then we'll kneecap our future selves.
The DFT paper is an example against AI 'strip-mining'. The paper introduces a new method, and researchers are already trying to improve on it. If anything, the OpenAI dump re-vitalized that branch of study.
Agreed. Basically, if you don't make any effort to understand the proofs and you just look at the final answer, it will look like this proof dump is "strip mining" entire branches of math. But this is a pretty short-sighted way of looking at the issue: there will be plenty of novel approaches to be uncovered here.