Amateur Armed with ChatGPT 'Vibe Maths' a 60-Year-Old Problem

Liam Price, a 23-year-old amateur with no advanced math training, used a ChatGPT Pro subscription (GPT-5.4 Pro) to solve a 60-year-old Erdős conjecture about primitive sets. He posted the solution to the Erdős Problems website. His occasional collaborator Kevin Barreto (Cambridge undergrad) recognized its significance and notified experts including Terence Tao (UCLA) and Jared Duker Lichtman (Stanford). Tao and Lichtman confirmed the solution was valid and have since shortened the proof.

The conjecture: as a primitive set's numbers approach infinity, the Erdős sum (a "score" for any primitive set of whole numbers where no element divides another) drops to exactly one. Lichtman had proven Erdős's first conjecture in his 2022 doctoral thesis — that the maximum possible Erdős sum only applies to the set of all primes — but got stuck on this second conjecture.

The AI used a formula "well known in related parts of math" that no one had applied to this type of question. Tao described it as a "mental block" — "The humans that looked at it just collectively made a slight wrong turn at move one." He noted the raw ChatGPT output was "actually quite poor" and required expert interpretation to extract the insight.

Price and Barreto had "jump-started the AI-for-Erdős craze late last year" using a free ChatGPT version on random open Erdős problems. An AI researcher gifted them Pro subscriptions.

Key people: Liam Price (amateur solver), Kevin Barreto (Cambridge undergrad, collaborator), Terence Tao (UCLA, verified and refined), Jared Duker Lichtman (Stanford, had proven the first conjecture), Paul Erdős (formulated the conjecture, deceased).

Tao's verdict: "What's beginning to emerge is that the problem was maybe easier than expected, and it was like there was some kind of mental block." And: "We have discovered a new way to think about large numbers and their anatomy" — suggesting broader applicability of the AI's approach.