Amateur uses ChatGPT to solve 60-year-old Erdős mathematics problem

A 23-year-old with no advanced mathematics training has cracked a 60-year-old problem that world-class mathematicians had failed to solve, using a ChatGPT Pro subscription. Liam Price got the solution in response to a single prompt to GPT-5.4 Pro and posted it on www.erdosproblems.com just over a week ago. The problem concerns special sets of whole numbers, called primitive sets, where no number in the set can be evenly divided by any other. Mathematician Paul Erdős came up with the Erdős sum, a score that can be calculated for any primitive set. He showed that the biggest the sum could be was about 1.6 and conjectured that this value must also hold for the infinite set of all prime numbers. Stanford mathematician Jared Lichtman proved Erdős right in 2022. Erdős also guessed that the lowest this score could be was exactly one, a limit the score would approach as the set's numbers approached infinity. Lichtman tried to prove this but got stuck like everyone else before him. Price was not aware of this history when he entered the problem into ChatGPT. The LLM took an entirely different route from the standard sequence of moves that previous researchers had used, applying a formula that was well known in related parts of math but which no one had thought to apply to this type of question. UCLA mathematician Terence Tao said the raw output of ChatGPT's proof was quite poor and required an expert to sift through and understand what it was trying to say. Tao and Lichtman have since shortened the proof to better distill the LLM's key insight. They already see other potential applications of the AI's cognitive leap.