ChatGPT Pro cracks 60-year-old Erdős problem with novel approach

A 23-year-old amateur named Liam Price prompted GPT-5.4 Pro with an open Erdős problem on a whim and got back what appears to be a genuine solution to a conjecture about primitive sets — collections of integers where no element divides another. The problem, which asks about the lower bound of the Erdős sum for sets of large numbers, had stumped Stanford mathematician Jared Lichtman and others who all started down the same blind alley.

What distinguishes this result from prior AI-on-Erdős hype is methodology. The LLM bypassed the standard opening move everyone else had tried and instead applied a formula well-known in adjacent areas of number theory but never previously connected to this class of problem. Terence Tao characterizes it as humans collectively making a wrong turn at move one, with the AI sidestepping the mental block.

The raw output was reportedly messy and required expert mathematicians to extract and refine the actual proof. Tao and Lichtman have since condensed it and believe the underlying technique may generalize to other problems about the structure of large numbers — a more durable contribution than the one-off solutions that have driven recent AI math headlines.