RESEARCH

Holy: OpenAI researchers report solving five (!) additional Erdős problems using an internal model, showcasing AI’s growing strength in deep mathematical reasoning.

Excitement for spud increases day by day. https://t.co/xss1rxAm6Z

— Chubby♨️ (@kimmonismus) 9 avril 2026

Holy: OpenAI researchers report solving five (!) additional Erdős problems using an internal model, showcasing AI’s growing strength in deep mathematical reasoning. Excitement for spud increases day by day. Mehtaab Sawhney (@mehtaab_sawhney) We’ve just released another paper solving five further Erdős problems with an internal model at OpenAI: arxiv.org/abs/2604.06609. Several of the proofs were especially enjoyable to digest while writing the paper. My personal favorite was the solution to Erdős Problem 1091. The question asks: if a graph G has chromatic number 4, while every small subgraph has chromatic number at most 3, must it contain an odd cycle with many diagonals? The internal model gives a very enlightening counterexample to this conjecture, and the proof was a pleasure to understand. For those so inclined, a really fun exercise is to try to reconstruct the proof from Figure 5 of the paper, which was of course produced by Codex. — https://nitter.net/mehtaab_sawhney/status/2042072817395757467#m

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