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

A 23-year-old amateur enthusiast, with the assistance of GPT-5.4 Pro, unraveled the Erdős mathematical conjecture that had been unsolved for 60 years (#1196). The model connected integer structures through interdisciplinary Markov processes, proposing a proof path that humans had never attempted.

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, OpenAI held an official podcast featuring researcher Sébastien Bubeck and Ernest Ryu in conversation with host Andrew Mayne, publicly explaining the event details and significance.

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

Solver Liam Price, 23, with no advanced mathematics training, occasionally collaborates with Kevin Barreto, a second-year mathematics student at Cambridge University. Price stated: “I didn’t even know what this problem was—sometimes I just throw Erdős problems to AI to see what it comes up with.”

In April 2026, on a Monday afternoon, 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 an in-depth report on April 24, and OpenAI’s official podcast on April 28 was a week later, providing a public explanation.

Mathematical breakthrough: Connecting integer structures via Markov processes, Tao comments “The first step humans took was wrong”

Erdős #1196 falls within the research scope of “primitive sets”—a collection of integers where no element divides another. Erdős’s conjecture states: as the elements of such sets approach infinity, the maximum of the “Erdős sum fraction” will drop exactly to 1.

GPT-5.4 Pro’s proof takes an approach “humans have never tried before”: linking the structure of integers (anatomy of integers) with Markov process theory. This interdisciplinary bridge was previously not part of anyone’s research path.

Fields Medalist and renowned mathematician Terence Tao has made two widely cited comments on this event. He described “This problem is different from others—humans have indeed seen it, but collectively, they took the wrong first step,” and added, “The significance of this contribution to the study of integer structures far exceeds just solving this particular Erdős problem.”

Another mathematician from Stanford University, Jared Duker Lichtman, stated that AI’s approach confirmed his long-standing intuition: there exists a “certain common unifying sense” among these types of problems.

OpenAI 4/28 Disclosure: Podcast discussion and subsequent verification

On April 28, OpenAI officially invited researcher Sébastien Bubeck and Ernest Ryu to discuss “AI’s role in mathematical research” with host Andrew Mayne on their podcast. OpenAI tweeted: “Earlier this month, a 60-year-old Erdős problem was solved with GPT-5.4 Pro. Now AI is proficient in mathematics—what will happen next?”

As of this writing, Price’s submitted proof remains in the community verification stage on erdosproblems.com and has not yet passed formal peer review; TheDecoder reported on April 15 that “formal verification is still ongoing.” The podcast revelation today is an external communication level, not an indication that the full mathematical proof has been verified—readers interested in follow-up can monitor thread #1196 on the Erdős Problems forum.

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