Aristotle leaps in math
Harmonic’s Aristotle model jumped from solving 10 verified Erdos problems to 117 in three months — a 10× increase — and the team says it’s aiming for a Millennium Prize‑level result by 2028. That’s a major signal for AI progress in formal mathematics. (x.com)
Harmonic was co‑founded by Robinhood CEO Vlad Tenev and Tudor Achim and publicly launched the Aristotle system in 2025, positioning the company around formalized mathematical reasoning. Harmonic has published that Aristotle returns Lean‑checked proofs and the company donated $300,000 to the Lean Focused Research Organization while offering $1,000,000 in sponsorships to mathematicians to accelerate formalization work. An arXiv writeup documents a Lean‑verified resolution of Erdős Problem #728 produced by a pipeline combining OpenAI’s GPT‑5.2 Pro with Harmonic’s Aristotle; the paper was posted in January 2026 and provides the formal Lean files and authorship details. Terence Tao publicly acknowledged that an AI‑generated proof was “more or less autonomous,” and researchers say the GPT‑5.2 + Aristotle pipeline produced a machine‑checkable proof that was then vetted by the community. Harmonic’s technical paper and GitHub repositories show Aristotle’s architecture: a Lean proof‑search component, an informal lemma generator, and a dedicated geometry solver used to produce the IMO‑level Lean proofs in 2025 (five of six problems), with the corresponding Lean files available on GitHub. Independent trackers and analysis projects report rapid growth in AI‑produced, Lean‑verified entries on Erdős problem collections and estimate that a large fraction of recent AI‑era solutions come with machine‑checked proofs, citing community audits and database updates.
