‘Aristotle’ AI cracks 30-year math problem

December 9, 2025

Aristotle, Harmonic’s AI system, independently solved a 30-year-old version of Erdős Problem #124 — what researchers are calling the first true step into the era of “vibe proving” mathematics.

The system reached the result in six hours and then formally verified the proof in Lean in just one minute. This was made possible by the new beta version of Aristotle, which combines stronger reasoning capabilities with a natural language interface for step-by-step proof writing.

Vilad Tenev, founder of Harmonic, describes “vibe proving” as a process where AI intuitively discovers the structure of a solution, which is then rigorously confirmed mathematically by machines. Harmonic’s progress comes after a $120 million investment and excellent results on IMO tests, placing the company alongside Google and OpenAI in the field of mathematical reasoning.

This is a step toward mathematical superintelligence — a world where AI generates and verifies proofs faster than humans can. Such tools could open the doors of advanced mathematics to a much wider audience and accelerate the solving of problems that have been out of reach for decades.

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