Start-up and OpenAI Technology Said to Help Solve an Erdos Problem

Earlier this month, the A.I. start-up Harmonic said its system, Aristotle, had solved an "Erdos problem" with help from OpenAI’s GPT-5.2 Pro, a development that some researchers described as evidence that A.I. can do academic research. Reactions were mixed. Some mathematicians and A.I.

researchers praised the work as surprising and useful, while others said the solution resembled earlier human work. Terence Tao of UCLA said the result "feels to me like a really clever student who has memorized everything for the test but doesn’t have a deep understanding of the concept." OpenAI’s vice president of science, Kevin Weil, had earlier posted that GPT-5 had found solutions to several long-open Erdos problems but deleted the post after researchers noted the system had identified existing solutions buried in decades of papers and textbooks.

Two mathematicians in Britain, Kevin Barreto and Liam Price, used GPT-5 to produce a solution and then used Harmonic’s Aristotle to verify it; Aristotle uses a specialized programming language to prove whether an answer is correct. The researchers said they nudged the systems when proofs fell short, and Thomas Bloom of the University of Manchester said that while the work was not high-level research, it was enough that he would consider suggesting publication if a graduate student produced it.

Researchers say modern A.I.

Key Topics

Tech, Harmonic, Aristotle, Openai, Erdos Problems, Terence Tao