A 23-year-old amateur with no advanced mathematical training has used ChatGPT Pro to solve a mathematical conjecture that has eluded experts for six decades, according to a report by Scientific American.
Liam Price used OpenAI’s latest large language model, GPT-5.4 Pro, to find a solution to a problem involving 'primitive sets'—collections of whole numbers where no number in the set can be divisible by another.
Price posted the solution to erdosproblems.com, a website dedicated to the mathematical puzzles left behind by the prolific mathematician Paul Erdős, just over a week ago.
While AI has recently been used to solve various Erdős problems, experts previously noted that many of those solutions lacked originality. However, this new discovery appears to utilize a method no human had previously conceived.
“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,” said Terence Tao, a mathematician at the University of California, Los Angeles.
Tao, who tracks AI's progress in mathematics, suggested the AI's success might stem from breaking a specific mental block. “What’s beginning to emerge is that the problem was maybe easier than expected,” he said.
A new approach to primitive sets
The problem concerns the 'Erdős sum,' a score calculated for primitive sets. Erdős conjectured that as the numbers in a set become larger, the score approaches a limit of exactly one.
While mathematician Jared Lichtman of Stanford University proved a related conjecture in 2022, the specific limit regarding larger numbers had remained unproven.
Price admitted he was not searching for a breakthrough when he prompted the AI. “I didn’t know what the problem was—I was just doing Erdős problems as I do sometimes, giving them to the AI and seeing what it can come up with,” Price told Scientific American.
“And it came up with what looked like a right solution,” he added.
Experts believe the LLM-conceived connection could have broader applications in mathematics, as the method used by the AI represents a departure from traditional human approaches to this type of problem.
