Claude Mythos from Anthropic Challenges OpenAI on the Erdős Problem

Advancements in artificial intelligence continue to push the boundaries of what is possible, and Claude Mythos from Anthropic is a striking example. According to Anthropic employees, Claude Mythos has managed to solve the famous Erdős unit distance conjecture, a combinatorial geometry problem that has remained unsolved since 1946. This achievement comes shortly after OpenAI also disproved the same conjecture.

Sholto Douglas, an engineer at Anthropic, shared on X that Claude Mythos solved the problem with a "cute and simple proof." This statement highlights what he sees as a "serious lag" in AI-driven mathematical discoveries. The team used a testing system built after the AI solved the Erdős problem #1196. Instances of Claude Code, equipped with Mythos, develop independent solutions before summarizing and sharing them. Mythos has often taken a different path than OpenAI's model.

Although mathematician Daniel Litt described Mythos's solution as "less good" than OpenAI's, he acknowledged that Mythos also found the solution proposed by OpenAI. Anthropic has published a version of the proof, prepared by Opus 4.7, to share these results.

Furthermore, Google DeepMind recently announced that its own AI-assisted system had solved nine Erdős problems. However, their approach, based on the formal proof language Lean, is considered less impressive by language model purists. Claude Code, while not a pure language model, is an agentic harness, demonstrating here its ability to compete with the best current AI systems.