Claude Mythos solves OpenAI's landmark Erdős problem with simple proof

Anthropic's Claude Mythos has solved OpenAI's landmark Erdős unit-distance conjecture with what an engineer called a "cute, simple proof," marking another AI-driven breakthrough in combinatorial geometry. The system, using isolated Claude Code instances that independently develop and distribute solution paths, reportedly also replicated OpenAI's original solution to the problem that had stood open since 1946. The achievement signals growing competition among AI labs in automated mathematical discovery, though some mathematicians rated Mythos's result slightly below OpenAI's.

Claude Mythos reportedly solves OpenAI's landmark Erdős problem with a "cute, simple proof" Anthropic employees say Claude Mythos can also solve OpenAI's "AI math milestone." OpenAI recently disproved the Erdős unit-distance conjecture https://the-decoder.com/openai-shifts-the-boundary-of-automated-reasoning-with-a-milestone-in-ai-mathematics-that-experts-are-now-unpacking/ , an open problem in combinatorial geometry since 1946. Anthropic engineer Sholto Douglas wrote on X https://x.com/ sholtodouglas/status/2059303540150137244 that Mythos solves it with a "cute, simple proof," a sign of "serious overhang" in AI-driven math discoveries. The team used a test system https://x.com/ alpoge /status/2059298567366513110 built after AI solved Erdős problem 1196 https://the-decoder.com/openais-gpt-5-4-pro-reportedly-solves-a-longstanding-open-erdos-math-problem-in-under-two-hours/ : isolated Claude Code instances with Mythos access receive the problem, develop solution paths, and then one instance summarizes and distributes them to further instances working independently. Mythos frequently took a different route than OpenAI's model. Mathematician Daniel Litt called https://x.com/littmath/status/2059309078812180877 the result "a bit worse" than OpenAI's, but Mythos reportedly found OpenAI's solution too. Anthropic published a proof version prepared by Opus 4.7 https://www-cdn.anthropic.com/files/4zrzovbb/website/ca35f196125c899a5ad11f011080202a652aef02.pdf . Google DeepMind also recently announced that an AI-assisted system solved nine Erdős problems https://the-decoder.com/google-deepminds-alphaproof-nexus-solves-decades-old-math-problems-for-a-few-hundred-dollars/ , though its approach relies on the formal proof language Lean, which is less impressive from an LLM purist's perspective. Then again, Claude Code is an agentic harness, not a pure LLM either https://the-decoder.com/frontier-radar-2-why-ai-productivity-gets-lost-between-benchmarks-and-the-balance-sheet/ . AI News Without the Hype – Curated by Humans Subscribe to THE DECODER for ad-free reading, a weekly AI newsletter, our exclusive "AI Radar" frontier report six times a year, full archive access, and access to our comment section. Subscribe now Douglas via X https://x.com/ sholtodouglas/status/2059303540150137244 | Levent via X https://x.com/ alpoge /status/2059298565093196012