AI now proving math

Mathematics is moving onto software that checks every step, and artificial intelligence is starting to help write those checked proofs. (microsoft.com) Those systems work inside theorem provers such as Lean, a programming language and proof assistant created at Microsoft Research in 2013 for machine-checkable mathematics. Lean’s community library, Mathlib, now contains more than 2 million lines of formalized mathematics, giving both researchers and AI systems a large stock of verified definitions and lemmas to build on. (microsoft.com) (lean-lang.org) In this setup, a proof is written more like code than chalkboard notes: every claim has to compile against precise rules. That makes formal math slower to write, but it also lets a computer reject gaps that a human referee might miss. (lean-lang.org) (microsoft.com) That formal layer has turned mathematics into a training ground for artificial intelligence reasoning. Google DeepMind said in July 2024 that AlphaProof and AlphaGeometry 2 solved four of six International Mathematical Olympiad problems, reaching a silver-medal score after the problems were translated into formal language. (deepmind.google) DeepMind later published the AlphaProof method in *Nature* on November 12, 2025, saying the system learned to find formal proofs with reinforcement learning and solved three of the five non-geometry Olympiad problems from the 2024 contest. The paper said the combined system needed multi-day computation for that medal-level result. (nature.com) (deepmind.google) Mathematicians are paying attention because formal proof is no longer just a way to verify finished work. Quanta reported on April 13, 2026 that researchers are increasingly using AI systems to suggest conjectures, search proof paths, and help produce new results inside formal systems. (quantamagazine.org) The shift has been building for several years through projects that showed formalization could handle real research mathematics. In July 2022, the Lean community announced the completion of the Liquid Tensor Experiment, a formal verification effort around work proposed by Peter Scholze. (leanprover-community.github.io) (quantamagazine.org) Researchers still describe the process as labor-intensive. Terence Tao said in a September 26, 2025 interview that formalization is “extremely tedious and time-consuming,” but he also said automation could change the field if it helps with the drudge work while keeping errors in check. (renaissancephilanthropy.org) That is why formal mathematics has become a test for frontier artificial intelligence systems as well as a tool for mathematicians. A model that can survive strict proof checking is doing more than producing plausible text; it is operating in a setting where wrong steps can be mechanically exposed. (nature.com) (microsoft.com) The next hurdle is speed and scale. Lean’s own project page says the goal is to reduce the overhead of formal proofs enough that writing them feels closer to ordinary mathematical prose, which would make AI-assisted proving less like a lab demo and more like daily research practice. (microsoft.com)