GPT-5.4 Pro Solves the 60-Year Erdős Conjecture #1196

According to OpenAI’s official announcement on April 28 and Scientific American’s in-depth report on April 24, a 60-year-old Erdős mathematical conjecture (No. #1196) was solved with the help of ChatGPT’s flagship reasoning model, GPT-5.4 Pro. On the same day, OpenAI formally explained the event’s details and significance to the public via an official Podcast, where researchers Sébastien Bubeck and Ernest Ryu spoke with host Andrew Mayne.

Event protagonist: 23-year-old amateur Liam Price

Solver Liam Price, 23, has no advanced math training and usually collaborates on research only occasionally with Kevin Barreto, a second-year student in the mathematics department at the University of Cambridge. Price describes: “I don’t know what the problem is—I just sometimes throw Erdős questions to AI and see what it comes up with.”

The process:

On a Monday afternoon in April 2026, Price inputs Erdős #1196 into GPT-5.4 Pro

After about 80 minutes of reasoning, the model provides a proof outline

Then it takes about another 30 minutes to organize it into a LaTeX paper

Price pastes the solution into the erdosproblems.com forum’s #1196 thread to submit it for community review

Scientific American’s report publication date is April 24, 2026; OpenAI’s April 28 Podcast disclosure is a one-week-later official version of the explanation.

Mathematical breakthrough: links integer structure with Markov processes, Tao says “the first step was already wrong by the humans who came before”

Erdős #1196 falls within the study of “primitive sets”—a group of integers in which no element divides any other. Erdős’s conjecture is that as the elements of these sets approach infinity, the maximum value of the “Erdős sum score” will drop exactly to 1.

GPT-5.4 Pro’s proof takes a route that “human mathematicians have never tried before”: it creates a connection between the anatomy of integers and Markov process theory. This cross-disciplinary bridge was not on anyone’s research path previously.

Prize-winning Fields Medalist and renowned mathematician Terence Tao made two widely cited comments on this event:

“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.”

“That would be a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdos problem.”

Another mathematician from Stanford University, Jared Duker Lichtman, also said that the path taken by the AI validated his long-held intuition: that there is “some kind of common unifying sense” among problems like these.

OpenAI’s 4/28 disclosure: Podcast discussion and subsequent verification

In the April 28 Podcast, OpenAI formally invited its researchers Sébastien Bubeck and Ernest Ryu to discuss with host Andrew Mayne “the role of AI in mathematical research.” OpenAI’s tweet, verbatim: “Earlier this month, an Erdős problem that had been open for 60 years was solved with help from GPT-5.4 Pro. What happens now that AI is getting good at math?”

As of the deadline for this article, the proof Price submitted is still in the community verification stage on the erdosproblems.com forum and has not yet passed formal peer review; TheDecoder’s April 15 report noted that “formal verification is still in progress.” OpenAI’s Podcast disclosure today is at the level of external communication and does not mean that complete mathematical proof verification has already been completed—readers who want to follow up can watch the Erdős Problems forum thread #1196.

The earliest appearance of this article about GPT-5.4 Pro solving the 60-year-old Erdős conjecture #1196 was on the Chain News ABMedia.