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

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

According to OpenAI’s official announcement on April 28 and a deep-dive report by Scientific American on April 24, a 60-year-old unsolved 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 also published an official Podcast episode featuring a conversation between researchers Sébastien Bubeck and Ernest Ryu and host Andrew Mayne, formally explaining the event’s details and significance.

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

Solver Liam Price is 23 and has no advanced mathematics training. He occasionally collaborates with Kevin Barreto, a second-year mathematics student at the University of Cambridge. Price said, “I don’t even know what the problem is—I just sometimes throw Erdős problems at AI to see what it comes up with.”

In April 2026, one 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 to the community for review. Scientific American published its in-depth report on April 24, and OpenAI’s official Podcast explanation came a week later, on April 28.

Mathematical breakthrough: connecting integer structures via Markov processes—Tao says “humans got the first step wrong”

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

GPT-5.4 Pro’s proof takes a path of the kind “humans have never tried”: it connects the anatomy of integers with Markov process theory. This interdisciplinary bridge was not on anyone’s research route before.

Two comments from Terence Tao, a Fields Medal winner and renowned mathematician, about this event have been widely cited. He described the problem as “different from others—humans have indeed seen it, but as a group they took the wrong first step,” and added that “the significance of this contribution to the study of integer structures goes far beyond merely solving this specific Erdős problem.”

Another mathematician at Stanford University, Jared Duker Lichtman, said that the approach taken by AI confirmed his long-held intuition: there is a “certain sense of unity” shared among problems like this.

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

On the April 28 Podcast, OpenAI officially invited OpenAI researchers Sébastien Bubeck and Ernest Ryu to speak with host Andrew Mayne about “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 that AI is good at math, what will happen next?”

As of the time of writing, the proof submitted by Price 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 ongoing.” OpenAI’s Podcast disclosure is at the level of public communication and does not mean the complete mathematical proof has been fully verified—readers who want to follow up can watch the Erdős Problems forum thread #1196.

• This article is reproduced 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