Math enthusiast converses with AI, resolves a 60-year-old unsolved problem

Explanation

In April 2026, Liam Price, a 23-year-old math enthusiast without advanced mathematical training, engaged in dialogue with OpenAI's "GPT-5.4 Pro" and was led to solve "Erdős Problem 1196," a difficult number theory problem that had remained unsolved for about 60 years. The problem, posed by mathematicians Erdős, Sárközy, and Szemerédi, concerns a conjecture about the properties of "primitive sets" (sets in which no number is a divisor of any other). The AI presented a unique approach using the von Mangoldt function, different from traditional methods, and the proof was formally verified using the mathematical proof assistant system "Lean." Fields Medalist Terence Tao also joined in the verification, and in May 2026 it was published on arXiv as a co-authored paper by eight people, including Price and Tao.