AlphaProof Nexus Solves Nine Erdős Problems

The breakthrough is less “AI replaces mathematicians” than a credible proof-search workflow where language models are continuously checked by a compiler.

• –The paper reports costs of a few hundred dollars per solved problem, so the widely repeated $100 figure is an oversimplification.
• –Lean mechanically verifies each proof step, sharply reducing hallucinated mathematical arguments.
• –A 9-of-353 success rate shows impressive capability but also clear limits; results concentrate in domains with mature formal libraries.
• –The simpler LLM-plus-compiler agent reproduced all nine Erdős solutions, suggesting stronger models may matter more than increasingly elaborate agent architectures.
• –DeepMind released the generated Lean proofs and natural-language proofs for inspection. [Results repository](https://github.com/google-deepmind/alphaproof-nexus-results)