23-year-old amateur solved a 60-year-old math problem using ChatGPT Pro — by finding a method no mathematician had discovered

Liam Price, a 23-year-old with no advanced mathematics training, used OpenAI's GPT-5.4 Pro to solve an Erdős conjecture about 'primitive sets' (collections of whole numbers where none divides evenly into another) that had stumped professional mathematicians for six decades. He submitted a single prompt to ChatGPT and posted the solution on www.erdosproblems.com just over a week ago.

The AI's approach was fundamentally different: instead of following the standard sequence of moves every human mathematician had tried, it applied a well-known formula from a related mathematical field that no one had thought to use for this problem type. Mathematicians Terence Tao and Jared Lichtman say the AI discovered a new way to think about how large numbers work — something humans had a 'mental block' preventing them from seeing.

For mathematicians and AI researchers, this proves LLMs can solve hard problems using genuinely novel methods, not just brute-force pattern matching. Lichtman believes this approach may unlock solutions to other clustered math problems he's intuited were connected. For ChatGPT Pro subscribers interested in open problems, it demonstrates the tool can generate professional-grade mathematical insights with a single prompt.