Claude Mythos Solves Erdős Unit-Distance Conjecture with Elegant Mathematical Proof

Summary

Claude Mythos, Anthropic's latest language model, has reportedly solved the Erdős unit-distance conjecture, a fundamental problem in combinatorial geometry that has remained open since 1946. The breakthrough demonstrates the accelerating pace of AI-assisted mathematical discovery and highlights competitive advances across the AI landscape.

Anthropric employed an innovative agentic approach where isolated Claude Code instances with Mythos access developed independent solution paths. Anthropic engineer Sholto Douglas called it a "cute, simple proof" and noted "serious overhang" in AI-driven mathematical discoveries—suggesting substantial remaining potential.

The solution differs from OpenAI's recent approach, though Mythos reportedly also independently found OpenAI's solution. Google DeepMind separately announced solving nine Erdős problems using formal proof languages, representing multiple viable approaches to AI-assisted mathematics.

• The suggestion of "serious overhang" indicates the field is still in early stages of AI-assisted mathematical breakthroughs

Editorial Opinion

This achievement marks a significant milestone in AI-assisted mathematics, demonstrating that agentic LLM approaches can compete effectively with both formal proof languages and traditional methods. The "cute, simple proof" and suggestion of "serious overhang" hint at rapid acceleration in mathematical discovery. The convergence of multiple AI systems solving decades-old problems—each through different methodologies—suggests we're entering a transformative era where AI becomes the standard approach for tackling previously intractable mathematical challenges.