An amateur used AI to solve a 60-year-old math problem

Liam Price (23), without advanced mathematical training, asked ChatGPT Pro and GPT-5.4 Pro a single question and obtained a solution to an Erdős problem that had gone unsolved for over 60 years. He posted the result on erdosproblems.com, and experts who had been tracking the problem took notice immediately.

The problem concerns primitive sets, in which no element divides another, and the Erdős sum computed for such a set. Erdős conjectured that the score decreases as elements grow larger, and that the maximum value would approach 1 as the set grows infinitely large, but a proof in this direction had long been stuck. This solution followed an entirely different path based on a connection conceived by the LLM, applying a formula known from related mathematics to this type of problem for the first time.

Terence Tao noted that all previous attempts had gotten stuck at a similar first step, while Jared Duker Lichtman said the draft proof produced by ChatGPT was rough and required human interpretation and organization. The two refined it into a shorter form, and while the result offers a new clue for rethinking large numbers and their structure, its long-term significance remains uncertain.