Large language models are increasingly capable of mathematical proofs. While AI struggled with basic tasks in 2022, by 2025 models achieved gold-medal performance in math olympiads. By 2026, AI began solving open problems, including the Erdős unit distance conjecture and the Jacobian conjecture, with OpenAI’s Astra model presenting 10 significant proofs in August 2026.
In September 2026, OpenAI announced a breakthrough regarding the Navier-Stokes equations, potentially solving one of the seven Millennium Prize Problems. This would mark the first such achievement in 20 years. Additionally, Anthropic reported the formalization of Fermat's Last Theorem in the Lean language, involving millions of lines of code.
The mathematical community is responding with initiatives like the Leiden Declaration, which provides guidelines for AI usage, emphasizing transparency and researcher responsibility. Projects like First Proof have been established to independently verify AI-generated results, as formal validation becomes critical due to the high volume of machine-generated output.
Mathematicians are debating the future of the field, as AI shifts the value from merely obtaining proofs to verifying and canonicalizing them. Experts like Terence Tao suggest rethinking mathematical processes, while others express concern over the 'gold rush' mentality, which may lead to low-quality publications and potential plagiarism of human research.
