80-minute breakthrough! 23-year-old amateur uses ChatGPT assistance to solve a 60-year-old math problem

With the assistance of GPT-5.4 Pro, a 23-year-old amateur enthusiast has unraveled an Erdős mathematical conjecture that had remained unsolved for 60 years (#1196). By linking integer structures through interdisciplinary Markov processes, the model has proposed a proof route that humans have never tried before.

According to OpenAI’s official announcement on April 28 and an in-depth report by Scientific American on April 24, an Erdős mathematical conjecture that had been hanging for 60 years (ID #1196) was solved with the help of ChatGPT’s flagship reasoning model GPT-5.4 Pro. The same day, OpenAI also used an official Podcast—featuring a conversation among researchers Sébastien Bubeck and Ernest Ryu and host Andrew Mayne—to publicly explain the event’s details and significance.

Main figure of the event: Liam Price, a 23-year-old amateur

The solver Liam Price is 23 and has no advanced mathematics training. In his day-to-day work, he occasionally collaborates with Kevin Barreto, a second-year student in the mathematics department at the University of Cambridge. Price said, “I didn’t even know what the problem was—I just sometimes throw Erdős problems to AI and see what it comes up with.”

In a Monday afternoon in April 2026, Price submitted the Erdős #1196 輸入 GPT-5.4 Pro，模型約 80 分鐘推理後給出證明思路，他再花約 30 分鐘把模型輸出整理為 LaTeX 論文，最後貼上 erdosproblems.com 論壇 #1196 thread for community review. Scientific American published its in-depth report on April 24, and OpenAI’s official Podcast explaining the matter to the public came a week later on April 28.

Mathematical breakthrough: Connecting integer structures via Markov processes; Tao remarks that “the first step humans took was wrong”

Erdős #1196 falls under the research scope of “primitive sets”—a group of integers such that no element can divide another. Erdős’s conjecture is that as the elements of such a set approach infinity, the maximum value of the “Erdős sum fraction” will fall to exactly 1.

GPT-5.4 Pro’s proof takes a “route that human mathematicians had never tried before” by making a connection between integer structure (anatomy of integers) and Markov process theory. This cross-disciplinary bridge was not on anyone’s research path before.

Two widely cited comments on the event came from Terence Tao, a Fields Medal winner and well-known mathematician. He described it as: “This problem is different from others—humans have indeed seen it, but collectively they took the wrong first step,” and he added that “the significance of this contribution to the study of integer structures goes far beyond solving this particular Erdős problem itself.”

Another mathematician from Stanford University, Jared Duker Lichtman, said that the path taken by AI confirmed his long-standing intuition: there is a kind of “shared sense of unity among problems like these.”

OpenAI reveals on 4/28: Podcast discussion and subsequent verification

In its April 28 Podcast, OpenAI officially invited researchers Sébastien Bubeck and Ernest Ryu to speak with host Andrew Mayne about “AI’s role in mathematical research.” OpenAI wrote in a tweet: “Earlier this month, a 60-year-old Erdős problem was solved with GPT-5.4 Pro. Now AI is already good at math—what happens next?”

As of the time of this article’s submission, the proof Price has submitted is still in the community verification stage on the erdosproblems.com forum and has not yet passed formal peer review. TheDecoder reported on April 15 that “formal verification is still ongoing.” OpenAI’s Podcast disclosure is at the level of external communication and does not mean that the full mathematical proof verification has been completed. Readers who want to follow up can pay attention to the Erdős Problems forum thread #1196.

• This article is reprinted with permission from: 《Chain News》
• Original title: 《23-year-old amateur uses ChatGPT to solve a 60-year-old math problem: cracked in 80 minutes》
• Original author: Elponcrab