Researchers are referring to the autonomous solution of a 30-year-old Erdæ issue by Aristotle, an AI system developed by Harmonic, as the first significant step into the "vibe proving" era of mathematics.

The specifics:

In six hours, Aristotle solved a variant of Erdæ Problem #124, which has been open since the 1990s. In just one minute, he officially verified the evidence in Lean.

Stronger reasoning and a natural language interface for exploring and writing step-by-step proofs were added to Aristotle's beta version to produce the final product.

Harmonic's founder, Vilad Tenev, referred to this as the emergence of "vibe proving," which is AI-driven proof discovery followed by machine-verifiable rigor.

In terms of mathematical reasoning, the development comes after Harmonic's $120 million investment and Aristotle's IMO gold performance, placing it among Google and OpenAI.

Another step toward mathematical superintelligence, where proofs are created, validated, and scaled at superhuman rates, is Harmonic's discovery. These kinds of tools can help increase access to complex mathematics, making it possible for anybody to participate in it instead of only professionals.

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