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A 23-year-old amateur used AI to help crack a 60-year-old math problem
High verification: Scientific American reporting with named expert sources, New Scientist coverage, and the public Erdős problems database. How we check stories
What happened
Paul Erdős left hundreds of open questions, now tracked on 1. Over the past year AI models have been credited with solving a number of them, with mixed results: Terence Tao keeps a public log of AI contributions2, and many early "wins" turned out to be less original than they first looked.
Joseph Howlett reported in Scientific American3 on April 24, 2026, that Price's result was different. On what Price described as an idle afternoon, he typed one of the problems into GPT-5.4 Pro using his ChatGPT Pro subscription, without knowing its history. A single prompt produced what looked like a correct proof, and Price posted it on the Erdős problems site.
The problem concerns "primitive sets": collections of whole numbers in which no number divides another. Stanford mathematician Jared Duker Lichtman had proved a related Erdős conjecture in his doctoral thesis but, like everyone before him, got stuck on this follow-up.
Why the experts were impressed
Price sent the proof to his occasional collaborator Kevin Barreto, a Cambridge math undergraduate, who saw it might be special and alerted experts. Tao told Scientific American that earlier attempts all began with the same standard moves, while the AI took a different route using a formula known in neighbouring areas of math. He called it "a nice achievement."
Price and Barreto weren't new to this. Scientific American reports that the pair helped start the trend of giving open Erdős problems to a free version of ChatGPT, and that an AI researcher later gifted them Pro subscriptions. New Scientist4 has also covered amateurs solving long-standing problems with AI.
Why this matters if you're choosing an AI plan
- Top-tier "Pro" models can do things cheaper tiers can't, on very hard reasoning problems.
- You still need someone who can check the work. This only counted because world-class mathematicians verified it.
- Most people don't need a Pro plan. For everyday writing, study or research help, a mid-priced plan is usually plenty.
Credits. Reporting by Joseph Howlett for Scientific American, with further coverage by New Scientist. The proof is by Liam Price using GPT-5.4 Pro, with Kevin Barreto, and was checked and refined by Terence Tao (UCLA) and Jared Duker Lichtman (Stanford). Up to Speed with AI has no relationship with the people or companies named, and nothing here suggests they endorse us or any AI plan.
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