Scientific American · 2026-04-24 · major
Amateur Solves 60-Year-Old Erdős Problem Using ChatGPT
A 23-year-old with no advanced math training used GPT-5.4 Pro to crack a 60-year Erdős conjecture on primitive sets, applying a formula professionals had overlooked. Terence Tao noted it broke a long-standing collective mental block.
A 23-year-old with no formal math training used GPT-5.4 Pro to crack a 60-year Erdős conjecture — and Terence Tao noticed.
What is it?
Liam Price, a 23-year-old with no graduate-level math background, prompted GPT-5.4 Pro with a decades-old unsolved conjecture from Paul Erdős about primitive sets — sets of integers where no element divides another. The AI surfaced a formula from a related area of mathematics that no one had thought to apply to this problem. Price used it to construct a proof, which was then reviewed and acknowledged by professional mathematicians including Terence Tao.
How does it work?
Erdős conjectured that the maximum 'score' of a primitive set approaches exactly 1 as numbers grow. GPT-5.4 Pro, prompted with the problem context, suggested applying an analytic formula from an adjacent field that converts the question into a tractable bound. Price iterated with the model over multiple sessions, developing the argument step-by-step and checking it against the mathematical literature.
Why does it matter?
This is one of the most concrete documented cases of an AI model enabling a non-expert to make a genuine mathematical contribution — not a routine calculation, but a problem that had resisted professional mathematicians for 60 years. It directly raises questions about how AI-augmented mathematics will work at scale and who gets to participate in research.
Who is it for?
AI researchers and mathematicians watching AI-augmented cognition
Try it
https://www.scientificamerican.com/article/amateur-armed-with-chatgpt-vibe-maths-a-60-year-old-problem/