https://www.scientificamerican.com/article/amateur-armed-with-chatgpt-vibe-maths-a-60-year-old-problem/

Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He’s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT Pro subscription, which gives him access to the latest large language models from OpenAI.

[snip]

“This one is a bit different because people did look at it, and the humans that looked at it just collectively made a slight wrong turn at move one,” says Terence Tao, a mathematician at the University of California, Los Angeles, who has become a prominent scorekeeper for AI’s push into his field. “What’s beginning to emerge is that the problem was maybe easier than expected, and it was like there was some kind of mental block.”

The question Price solved—or prompted ChatGPT to solve—concerns special sets of whole numbers, where no number in the set can be evenly divided by any other. Erdős called these “primitive sets” because of their connection to similarly indivisible prime numbers.