23-year-old amateur + ChatGPT solved a 60-year-old math problem
23-year-old amateur + ChatGPT solved a 60-year-old math problem
Liam Price typed Erdős Problem #1196 into GPT-5.4 Pro. One prompt. The AI thought for 80 minutes. It returned an answer no one found in six decades.
Erdős Problem #1196. Open since 1965. Posed by Paul Erdős, András Sárközy, and Endre Szemerédi - three of the greatest mathematicians of the 20th century. It concerns primitive sets - collections of integers where no number divides any other.
For 60 years no one cracked it.
What happened
Liam Price - a 23-year-old amateur mathematician - typed the problem into ChatGPT. Specifically: GPT-5.4 Pro. The model reasoned for 80 minutes and produced an answer. He posted the result on erdosproblems.com.
Terence Tao - Fields Medal winner, one of the greatest living mathematical minds - reacted. He called it a “nice achievement” with a cautious note that the long-term significance remains unclear.
The most interesting part
The AI didn’t invent anything new. It took a 90-year-old mathematical technique - Markov chains with von Mangoldt weights - and applied it where no one had thought to. Lichtman and Tao suspect this approach could unlock related problems in number theory following similar patterns.
This is a new category of intelligence. AI doesn’t think novel thoughts. AI connects dots we missed.
My perspective
It’s the first time in history AI entered academic mathematics at the level of publishable research. This isn’t about “AI writing a high-school exam.” It’s about AI solving problems considered unsolvable.
Next question - climate? Diseases? What can AI solve through “dot connecting” in fields where humanity got stuck?
Sources
- Scientific American - “Amateur armed with ChatGPT ‘vibe maths’ a 60-year-old problem”
- Techmeme - “An amateur solved a 60-year-old Erdős problem using a single GPT-5.4 Pro prompt; Terence Tao says it’s a ‘nice achievement’” (Apr 26, 2026)
- OpenAI X post - “Earlier this month, an Erdős problem that had been open for 60 years was solved with help from GPT-5.4 Pro”
- k4i.com - “GPT-5.4 Solves the Erdős Problem”
- Erdős Problems forum thread #1196