Harmonic AI Solves 4 30-Year-Old Math Problems: The Dawn of the AI Math Era
- Harmonic’s Aristotle AI autonomously solves 4 Erdős problems
- Problem #728 is the first Erdős problem solved completely autonomously by AI
- Fields Medal winner Terence Tao personally verified the proof
What happened?
Aristotle AI, developed by math AI startup Harmonic, solved four unsolved Erdős problems in a row during the month of January 2026.[arXiv] The Erdős problems are a collection of 1,133 challenging problems left by the legendary Hungarian mathematician Paul Erdős. Of these, 680 remained unsolved.
The most notable achievement is Problem #728. On January 4, Kevin Baretto published a proof using Aristotle, and on January 6, formal verification was completed using the Lean 4 programming language.[Hacker News] This is the first case of AI solving an Erdős problem completely autonomously without human assistance.
Subsequently, problems #729, #397, and #124 were solved in succession. Problem #124 had been unsolved for 30 years since the 1990s, but Aristotle solved it in just 6 hours.[36Kr]
Why is this important?
AI solving math problems is not new. DeepMind’s AlphaEvolve also outperformed humans in over 50 math puzzles. However, Aristotle’s distinguishing feature is formal verification.
Existing LLMs produce plausible answers but cannot avoid hallucinations. Aristotle generates mathematically perfect proofs through the Lean 4 proof assistant. Fields Medal winner Terence Tao’s review and approval of the proof for Problem #397 in just one day is also thanks to this verifiability.
Harmonic received $120 million in Series C funding at a valuation of $1.45 billion in November 2025. In January 2026, Nvidia’s NVentures even joined as an investor.[SiliconANGLE]
What happens next?
Harmonic’s co-founders Vlad Tenev (Robinhood CEO) and Tudor Achim aim for mathematical superintelligence. Mathematical verification technology is expected to expand into coding, chip design, and safety-critical software verification.
However, Terence Tao warned that the currently solved problems are the lowest-hanging fruit. These are problems that can be solved with standard techniques and are far from true mathematical breakthroughs. AI still relies on humans for problem framing and expert verification.
Frequently Asked Questions (FAQ)
Q: How does Aristotle AI solve math problems?
A: Aristotle combines reinforcement learning, Monte Carlo tree search, and the Lean 4 formal language. It transforms math problems in natural language into formally verifiable proofs. GPT-5.2 sometimes collaborates by generating initial proofs, which Aristotle then formally verifies with Lean.
Q: What kind of company is Harmonic AI?
A: It is a Palo Alto-based startup founded in 2023. Robinhood CEO Vlad Tenev is the co-founder and chairman of the board, and Tudor Achim is the CEO. It was valued at $1.45 billion in Series C funding, with investments from Nvidia, Sequoia, and Index Ventures.
Q: What are Erdős problems?
A: They are a collection of mathematical challenges posed by Hungarian mathematician Paul Erdős throughout his life. Currently, 1,133 have been cataloged, 279 have been solved, and 680 remain unsolved. They cover various fields such as number theory, combinatorics, and graph theory.
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References
- Resolution of Erdős Problem #728: a writeup of Aristotle’s Lean proof – arXiv (2026-01-06)
- Harmonic AI raises $120M at $1.45B valuation – SiliconANGLE (2025-11-25)
- AI Solved 30-Year Math Problem in 6 Hours – 36Kr (2026-01-14)