AlphaProof
Google DeepMind's reinforcement-learning system that writes formally verified math proofs in Lean.
Overview
AlphaProof is a Google DeepMind reinforcement-learning system that proves mathematical statements within the Lean 4 formal theorem prover, so every step is machine-checked. Paired with AlphaGeometry 2, it reached silver-medal-standard performance at the 2024 International Mathematical Olympiad, solving several of the hardest problems including the number-theory Question 6. The research was published in Nature. AlphaProof is a research system, not a public product — there is no app or self-serve access.
Pricing
Pricing shown for reference only. These figures reflect RECATOOLS research as of 12 Sep 2026 and may be out of date or incomplete. This is not financial or purchasing advice — always confirm the current price on the provider’s official website before making any decision.
What you can produce with AlphaProof
- Read how a reinforcement-learning system produces proofs inside Lean 4, machine-checked at every step
- Study the silver-medal International Mathematical Olympiad result it reached with AlphaGeometry 2
- Follow formal-methods research where proofs are verified rather than plausible
- Cite it in work on automated theorem proving
- Do not look for a signup: this is a DeepMind research system, not a product
- Judge it by scientific reception, because there are no users to review it
What this is for: Automatically finding and formally verifying rigorous mathematical proofs inside the Lean theorem prover.
Who this is for: Mathematics and AI researchers interested in automated reasoning and formal verification.
Availability: A DeepMind research system with published results in Nature — not a public product; there is no app or self-serve access.
What people say
AlphaProof is a DeepMind research system, not a consumer product, so its "reviews" are its scientific reception, which has been strong. Paired with AlphaGeometry 2, it reached silver-medal standard at the 2024 IMO (28 points, solving several of the hardest problems including Question 6), and its scoring was overseen by Fields Medallist Tim Gowers and IMO gold medallist Joseph Myers. Terence Tao and others publicly praised it for expanding the boundaries of AI in mathematics. The method was published in Nature in November 2025.
Mathematicians also voiced substantive criticism. Kevin Buzzard (Imperial) pointedly asked whether these systems have told us anything new, and concluded they haven't. The solutions apply known techniques to neglected problems, not mathematical creativity. Others flagged the enormous compute cost (test-time reinforcement learning per problem plus tens of thousands of TPU-days to train), likening it to "national-laboratory-scale" apparatus that ordinary researchers cannot reproduce.
There was also transparency criticism: DeepMind announced the result more than a year before publishing peer-reviewed methods, and the wider math community has since debated heavy AI use, including a mathematicians' declaration urging restraint. Impressive and rigorous, but costly, closed for a long stretch, and not yet creative.
Summary of public user & expert reviews, compiled by RECATOOLS.
About this listing
This entry was compiled from publicly available data including AlphaProof's official website, press releases, documentation, and reputable third-party publications. RECATOOLS is not affiliated with AlphaProof unless explicitly stated.
Third-party AI tools update their pricing, features, availability, and policies frequently. Information here may be outdated by the time you read this — we make reasonable efforts to keep listings current, but cannot guarantee absolute accuracy.
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