AI enters mathematics: where things stand

In recent months artificial intelligence has started producing results the mathematical community didn't expect this soon. In May 2026 an OpenAI model solved the unit distance conjecture, a problem that had been open for decades; in August the same team published ten more results on long-standing problems in mathematics and theoretical computer science. Competitions tell the same story of rapid progress: while in 2024 the first systems needed human assistance to tackle Math Olympiad problems, in 2025 Gemini Deep Think competed fully autonomously and won a gold medal.

But how certain are these results, really?

The answer depends on how the proof is verified. The most rigorous systems, like DeepMind's AlphaProof, don't rely on the language model's fluency: the model proposes each step of a proof in a formal language (Lean), and a separate symbolic verifier — a deterministic compiler, not a neural network — mechanically checks every step. The proof is accepted only if the verifier finds no errors: zero margin of trust in how plausible the generated text sounds. It's the same principle behind how AlphaZero plays chess: the network proposes and evaluates moves, but it's the rules of the game that determine whether a move is valid.

Not every result goes through this kind of verification, though. Gemini Deep Think's gold medal at the Olympiad was produced and graded in natural language, by human graders — with the same standard, and the same possible margin of error, used to grade a student's proof.

Not everyone is looking only at the results. Terence Tao, a Fields Medalist, devoted his ICM 2026 lecture to a different question: not how good AI will become, but what the actual goals of mathematical research are, and who gets to decide how it's integrated into the discipline.

Further reading: - Ten advances in mathematics – OpenAI - The AI Revolution in Math Has Arrived – Quanta Magazine - Mathematics in the age of AI – Terence Tao (ICM 2026)