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Claude Mythos reportedly solves OpenAI's landmark Erdős problem with a "cute, simple proof"

Claude Mythos reportedly solves OpenAI's landmark Erdős problem with a "cute, simple proof"

AI researchmathematics The Decoder

Anthropic's Claude Mythos reportedly solved OpenAI's recently disproven Erdős unit-distance conjecture with a "cute, simple proof," demonstrating independent AI-driven math discovery capabilities.

What: Anthropic engineer Sholto Douglas stated that Claude Mythos solved the Erdős unit-distance conjecture, an open combinatorial geometry problem since 1946, with a "cute, simple proof," mirroring OpenAI's recent achievement. Although Daniel Litt noted Mythos's initial solution was "a bit worse" than OpenAI's, it also reportedly found OpenAI's solution.

Why it matters: This suggests a "serious overhang" in AI's capacity for novel mathematical discoveries, as multiple frontier models are independently achieving breakthroughs in complex, long-standing problems, even when using different approaches.

Decoder

Erdős unit-distance conjecture: A famous unsolved problem in combinatorial geometry, posed by Paul Erdős in 1946, concerning the maximum number of unit distances that can be formed by a set of n points in a plane.
Combinatorial geometry: A branch of mathematics that combines aspects of combinatorics and geometry, dealing with finite or discrete collections of geometric objects.
Overhang: A term often used in economics or technology to describe a situation where there is a significant amount of untapped potential or unreleased capability that could impact future developments.
Lean (formal proof language): A proof assistant and programming language designed for formally verifying mathematical proofs and software, distinct from natural language model approaches.

Original article

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, an open problem in combinatorial geometry since 1946. Anthropic engineer Sholto Douglas wrote on X 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 built after AI solved Erdős problem #1196: 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 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.

Google DeepMind also recently announced that an AI-assisted system solved nine Erdős problems, 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.

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