Harmonic
A maths model that outputs formally verified Lean 4 proofs, so the answer is checked rather than merely plausible.
Highlights
- Outputs solutions as Lean 4 proofs that a formal verifier can check line by line
- Aristotle consumer app (iOS) for step-by-step math problem solving
- Public Aristotle API for mathematicians, researchers, and students
- Mathematical Superintelligence (MSI) approach aimed at hallucination-resistant reasoning
- Gold-medal-level result on the 2025 International Mathematical Olympiad (5 of 6 problems)
- Reported 96.8% on the VERINA code-verification benchmark
- Flags inconsistencies and unproven steps instead of asserting unverified answers
- Trained substantially on synthetic, formally checked math proofs
External link — opens harmonic.fun in a new tab. Harmonic is a third-party product; we are not affiliated with it.
About Harmonic
What it is
Harmonic builds Aristotle, a mathematical reasoning model that returns solutions as proofs in the Lean 4 language, which a formal verifier can then check line by line. That is a different guarantee from a chatbot producing convincing prose about a proof. There is a consumer iOS app for step-by-step problem solving and a public API for mathematicians, researchers and students.
Why it's different
This addresses the single worst property of language models in mathematics: they produce wrong answers in exactly the register of right ones, and a plausible-looking proof of a false statement is worse than no answer. Formal verification removes that failure mode entirely — if the verifier accepts it, it is correct, full stop. Nothing else in consumer maths tooling offers that. The limits follow from the method. Formalisation is slow and covers a narrower range of mathematics than a chatbot will happily discuss, and problems that resist formal statement resist Aristotle. It is strongest where rigour matters most and weakest on the informal reasoning that makes up most of mathematical practice.
How people use it
It is used by people for whom being certain matters more than being fast: researchers checking a step, students who want to know a solution is actually right rather than confident, and anyone already working in Lean. For competition-style and formally stated problems it is in a different class from general chatbots. For a question like explain why this is true in plain language, a general model remains the better tool.
Written by the n3os team. We are not affiliated with Harmonic.
This listing was written from public information, without Harmonic’s involvement. If you own it and something here is wrong — or you would rather not be listed at all — email us and we will correct or remove it.
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