23-Year-Old Uses ChatGPT to Crack 60-Year Math Problem

Liam Price isn't a mathematician. He's 23 years old, has no advanced training, and spends his free time feeding math problems to ChatGPT just to see what happens.

Last week, one of those casual experiments cracked a 60-year-old problem that has defeated some of the brightest minds in mathematics. Price typed a single prompt into ChatGPT Pro, and the AI responded with a solution no human had ever considered.

The problem came from Paul Erdős, a legendary mathematician who left behind hundreds of unsolved puzzles. This particular question dealt with "primitive sets," special collections of whole numbers where none can be evenly divided by any other.

Erdős had proven the maximum "score" for these sets was about 1.6. He then guessed the minimum score would approach exactly one as the numbers got infinitely large. Proving this seemingly simple claim had stumped experts for decades.

Price wasn't aware of any of this history. "I was just doing Erdős problems as I do sometimes, giving them to the AI and seeing what it can come up with," he says. He sent the output to his collaborator Kevin Barreto, who immediately recognized they'd stumbled onto something significant.

The raw proof ChatGPT generated was messy and required expert translation. But buried in the AI's work was a genuinely new approach using a formula from a different area of math that no one had thought to apply here.

Terence Tao, a Fields Medal winner at UCLA who tracks AI progress in mathematics, examined the proof with fascination. "The humans that looked at it just collectively made a slight wrong turn at move one," he explains. The AI simply didn't have that mental block.

Jared Lichtman at Stanford had tried to solve this exact problem as part of his doctoral thesis in 2022 and failed. Now he's excited because the AI's method confirms an intuition he'd held since graduate school about how certain math problems connect.

The Ripple Effect

This isn't just about one solved puzzle. Tao and Lichtman are already exploring how ChatGPT's insight might apply to other long-standing questions in number theory.

"We have discovered a new way to think about large numbers and their anatomy," Tao says. The AI found a bridge between mathematical concepts that human experts hadn't seen, despite years of study.

Price and Barreto sparked this wave of AI-assisted math solving late last year by casually feeding ChatGPT random problems from an Erdős database. An AI researcher, impressed by their "vibe mathing" approach, gifted them both premium subscriptions to keep experimenting.

The breakthrough suggests that sometimes fresh eyes matter more than expertise, and the freshest eyes of all might belong to something that doesn't think like us at all.