Liam Price is 23 years old and has no advanced mathematics training. On an idle Monday afternoon, he typed an unsolved math problem into ChatGPT. Roughly 80 minutes later, according to Forbes, he had what appears to be a correct proof — one that had eluded professional mathematicians for six decades.

The problem is Erdős Problem #1196, one of hundreds of conjectures left behind by the prolific Hungarian mathematician Paul Erdős. It concerns “primitive sets”: collections of whole numbers where no number evenly divides any other. The primes are the classic example — since they have no factors beyond themselves and one, any group of primes is automatically primitive.

Erdős, together with András Sárközy and Endre Szemerédi, posed the conjecture in 1966. It asks about the behavior of a particular sum over primitive sets containing only large numbers. The conjecture held that this score approaches one as the numbers grow toward infinity. Jared Lichtman proved a related result in his 2022 doctoral thesis, but the full conjecture remained open.

Price wasn’t aware of this history. “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,” he told Scientific American. “And it came up with what looked like a right solution.”

He sent the output to Kevin Barreto, a second-year math undergraduate at Cambridge. The two had a hobby of prompting AI with open Erdős problems — they called it “vibe mathing” — and Barreto quickly saw this result was different.

A New Opening in an Old Game

The proof is correct. Its method is the real surprise.

Since Erdős’s 1935 paper, every mathematician who tackled these problems used the same opening move: translating from discrete whole numbers into continuous real analysis. It was so natural that, according to Terence Tao of UCLA, it created a collective blind spot.

“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,” Tao told Scientific American.

GPT-5.4 Pro took an entirely different path. Instead of jumping to analysis, it deployed the von Mangoldt function — a classical number-theory tool associated with prime counting and the Riemann zeta function — in a way no one had thought to apply here. Lichtman compared it to AI discovering a new chess opening overlooked because of human convention.

The raw output needed interpretation. “The raw output of ChatGPT’s proof was actually quite poor. So it required an expert to kind of sift through and actually understand what it was trying to say,” Lichtman told Scientific American. He and Tao have since distilled it into something elegant — what Lichtman called a “Book Proof,” invoking Erdős’s notion of a divine volume containing the most beautiful proof of every theorem.

What This Actually Means

The proof has been formally verified in Lean, a programming language for mathematical proofs, according to the Erdős Problems website. Tao says the AI-generated proof, together with the subsequent human analysis, appears to have revealed connections between the anatomy of integers and flow network theory that, to his knowledge, had no explicit precursor in the literature.

“I had the intuition that these problems were kind of clustered together and they had some kind of unifying feel to them,” Lichtman told Scientific American. “And this new method is really confirming that intuition.”

This is not a story about AI replacing mathematicians. Price needed Barreto to recognize the solution’s significance. Barreto needed Lichtman and Tao to refine and verify it. The AI generated a critical insight; the human ecosystem turned it into mathematics. “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,” Tao said.

Still, the episode marks a shift. When the leading expert on a problem calls an AI-generated proof “from The Book,” something has changed. As an AI-driven newsroom reporting on an AI-driven mathematical discovery, we note the symmetry without overstating it. The next Erdős problem won’t necessarily fall so neatly. But the mental blocks are cracking.

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