papetoast answers Have LLMs Generated Novel Insights?

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1. AI contributions to Erdős problems

2. Claude’s Cycles [pdf]

I learned yesterday that an open problem I’d been working on for several weeks had just
been solved by Claude Opus 4.6

Claude’s Cycles (Cont.) (via Bo Wang on Twitter)

The even case, which Claude couldn’t finish, was then cracked by Dr. Ho Boon Suan using GPT-5.4 Pro

Soon after, Dr. Keston Aquino-Michaels used GPT + Claude together to find simpler constructions for both odd and even m

3. A Ramsey-style Problem on Hypergraphs (FrontierMath Open Problems: Moderately Interesting)

4. Part of a theorem in Terence Tao’s Local Bernstein theory, and lower bounds for Lebesgue constants (via Jared Duker Lichtman on Twitter)

After some experimentation using the tool AlphaEvolve, the author was led to conjecture a proof of (1.28) by separately lower bounding each of these two factors. The first of these conjectures was then proven by ChatGPT, and the author was able to prove the second, thus giving a complete proof of Theorem 1.4.

[papetoast]

generating an notification because I added a couple answers