When writing math papers, many (but unfortunately not all) mathematicians go through a post-processing step, where they take their ideas and proofs, and try to reduce them to simple and reusable core ideas that can be understood by the reader. Good writers will often also provide some representative examples that guided the proofs, explaining why various intermediate results can't be strengthened and why the proof can't be made much shorter without inventing new techniques. If AI-generated proofs were required to go through such a post-processing step before being published, that would go a long way towards improving the situation.
replyIt's funny that seems like a step the human mathematicians would want, and (at least for now) might still outperform the machines on. In the same way that, eg, the notebooks of Galois contained the core breakthroughs in a messy form, and generations after him simplified and synthesized those ideas, until you finally have books and videos accessible to undergraduates.
replyOne proposal that Tao hints at is to not rush to announce solutions. Instead maybe the AI companies should work privately with the subject matter experts on how to communicate the discoveries.
replyWell, they could ask frontier labs to stop publishing math results. I find it telling that they stop short of explicitly doing this.
replyIf frontier labs had chosen to go the path of offering to assist in existing endeavors, helping to build knowledge alongside researchers in ongoing projects and following ethical and professional research standards, we wouldn't be having this discussion at all; everyone would be stoked. Instead we have companies that disgracefully try to scoop researchers and fail to properly attribute earlier work and instead rebrand it as their own (what we normally call plagiarism) to make marketing material.
replyThis sort of nonsense makes me root for the AI companies to set the edifice of organized math on fire.
replyIt would be too transparently ridiculous.
replyhaving labs open their research: what harness system they used, what types of problems they tackled, which problems success and which fail, how they success and fail so we have a better idea of what tasks LLM are currently good at
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