Harmonic Math's Aristotle AI Proves Version of 30-Year-Old Erdos Problem #124

San Francisco, CA – Harmonic Math, an AI startup co-founded by Robinhood CEO Vlad Tenev, announced a significant milestone in artificial intelligence and mathematics: its AI model, Aristotle, has reportedly proven Erdos Problem #124. The problem, which has been open for nearly 30 years since its conjecture in the paper "Complete sequences of sets of integer powers" in Acta Arithmetica, was solved within the Lean theorem prover. This development, spearheaded by Boris Alexeev using a beta version of Aristotle, has ignited discussions about the accelerating progress towards "mathematical superintelligence."

Vlad Tenev, in a recent social media post, expressed optimism about the breakthrough. "We are on the cusp of a profound change in the field of mathematics. Vibe proving is here," Tenev stated, adding that he is "confident it will change and dramatically accelerate progress in mathematics and all dependent fields." Aristotle, which recently achieved gold medal-level performance at the 2025 International Mathematical Olympiad by solving five of six problems, integrates formal verification with informal reasoning and features a natural language interface.

However, the claim of solving the full Erdos Problem #124 has been met with nuance by some mathematicians. Thomas Bloom, maintainer of the Erdos Problems website, acknowledged the AI's impressive solution but clarified that it pertains to a "simpler version" of the problem. "This is a nice solution, and impressive to be found by AI, although the proof is (in hindsight) very simple," Bloom commented, noting that the AI's solution might not align with the problem as posed in certain academic papers. He suggested keeping the original, more complex version of the problem open.

The debate centers on different formulations of Erdos Problem #124, particularly regarding the inclusion of '1's in sequences and specific greatest common divisor (GCD) conditions. While Aristotle successfully formalized a version of the conjecture, experts like Bloom and others on mathematical forums indicate that the version solved might be an "easier" variant that had not resisted extensive efforts from mathematicians. Despite this distinction, the ability of an AI to autonomously generate a formal proof for any version of a long-standing problem represents a notable advancement in automated theorem proving.

Harmonic Math recently secured $120 million in Series C funding, valuing the company at $1.45 billion, with the stated goal to accelerate the development and commercialization of Mathematical Superintelligence (MSI). The company envisions Aristotle as a tool that will assist mathematicians and researchers across various fields, from cryptography to scientific computing, by automating the arduous task of formalizing mathematical arguments and potentially unlocking new avenues for discovery.