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 the Erdős mathematical conjecture that had remained unsolved for 60 years (#1196). The model connected integer structures via interdisciplinary Markov processes, proposing a proof path that humans had never tried.

According to OpenAI’s official announcement on April 28 and an in-depth report by Scientific American on April 24, a 60-year-old Erdős mathematical conjecture (ID #1196) was solved with the help of the flagship reasoning model GPT-5.4 Pro. On the same day, through an official Podcast, OpenAI also provided details about the event and its significance to the public via a conversation involving researchers Sébastien Bubeck and Ernest Ryu, with host Andrew Mayne.

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

Solver Liam Price is 23, with no advanced mathematics training; he occasionally collaborates on research with Kevin Barreto, a second-year student in the Department of Mathematics 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.”

On an afternoon Monday 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, while OpenAI’s official Podcast explanation came a week later on April 28.

Mathematical breakthrough: Connecting integer structures via Markov processes—Tao calls it “the first step humans took was wrong”

Erdős #1196 falls within the research scope of “primitive sets”—a class of integers such that no one element can be divided by another. Erdős’s conjecture is that as the elements of such a set approach infinity, the maximum value of the “Erdős sum score” will drop to exactly 1.

GPT-5.4 Pro’s proof takes the “route that human mathematicians had never tried before”: it links the anatomy of integers with Markov process theory. This interdisciplinary bridge was not on anyone’s research path before.

Two comments about this event from Fields Medalist and renowned mathematician Terence Tao are widely cited. He described the problem as “different from others—humans have indeed looked at it, but as a group they got the first step wrong,” and added that “the significance of this contribution to the study of integer structures far exceeds simply solving this specific Erdős problem.”

Jared Duker Lichtman, another mathematician at Stanford University, said the AI’s approach validated his long-standing intuition: that there is “some kind of shared, unifying sense among these problems.”

OpenAI 4/28 Reveal: Podcast discussion and subsequent verification

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

As of the time of this writing, the proof submitted by Price is still in the community verification stage on erdosproblems.com and has not yet passed formal peer review; TheDecoder’s April 15 report said that “formal verification is still ongoing.” OpenAI’s Podcast reveal today is at the level of external communication and does not mean the complete mathematical proof has already been verified—readers who want to track follow-ups can check the Erdős Problems forum thread #1196.

• This article is republished 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