Harmonic is forging the world's most advanced mathematical reasoning engine through its flagship model Aristotle, which produces formally verified solutions to complex mathematical problems. Unlike language-based AI systems prone to hallucinations, Aristotle generates output guaranteed to be correct with interpretable reasoning chains verified through the Lean 4 proof language and its mathematical library Mathlib. The system demonstrated this capability by achieving gold medal performance on the 2025 International Mathematical Olympiad, producing complete formal proofs for five of six competition problems.

Aristotle combines formal verification with informal reasoning capabilities, allowing it to flexibly plan and leverage the broader corpus of mathematical knowledge while maintaining rigorous verification standards. The system employs a highly parallel Monte Carlo Graph Search using transformer models for policy and value functions, guided by informal reasoning to develop proofs one step at a time. This architecture enables Aristotle to solve problems across algebra, number theory, combinatorics, and geometry at Olympiad level while ensuring every solution is machine-checkable and free from logical errors.

The platform is designed for mathematicians, researchers, and practitioners in quantitative fields who require provably correct solutions. Aristotle can formalize natural language mathematical statements into Lean code, generate formal proofs, and translate results back to human-readable explanations. The system has already been used by researchers to prove open conjectures in cryptography and topology, find errors in AI-generated proofs, and accelerate progress in theoretical mathematics. Applications extend to safety-critical domains including aerospace, chip design, industrial systems, and healthcare where software reliability is paramount.

Harmonic provides access to Aristotle through multiple channels including iOS and Android mobile applications, a web interface, and an API for enterprise integration. The company offers mathematician sponsorships including Principal Investigator Awards with funding up to $100,000 for high-impact research projects and Rising Mathematician Awards for undergraduate researchers exploring formal mathematics tools. The platform supports both automated theorem proving and interactive proof development with features for canceling and resuming computation jobs.