ChatGPT solves 60-year-old mathematics problem: a 23-year-old amateur with no mathematics background succeeded in the challenge with GPT-5.4 Pro

Liam Price, 23, does not have any advanced mathematics training background, but he used ChatGPT Pro (GPT-5.4 Pro) to solve an Erdős problem that has troubled mathematicians for 60 years with just one hint. Professor Tao Zhexuan confirmed that his solution is effective and novel, which indicates that AI is enabling ordinary people to have research capabilities that surpass those of professional scholars.

Core conclusion

On April 24, 2026, "Scientific American" reported a milestone event: a 23-year-old young man named Liam Price, who did not have any advanced mathematics background, used only a ChatGPT Pro subscription (GPT-5.4 Pro) to solve an Erdős mathematical problem that no one had been able to solve for 60 years. Professor Terence Tao, a Fields Medal winner at the University of California, Los Angeles, confirmed the effectiveness of the solution and pointed out that AI uses a new method that humans have never thought of.

Key Points

Event Time: Published in Scientific American on April 24, 2026
Protagonist: Liam Price, 23 years old, zero professional training in mathematics
Tool: ChatGPT Pro (GPT-5.4 Pro), single prompt word
Achievements: Cracking the Erdős conjecture about "primitive sets"
Industry Comments: Professor Terence Tao confirmed that the solution is effective and admitted that "the human collective took the wrong direction in the first step."
Heat value: Second on Hacker News homepage, 755 likes, 539 comments

Background and core events

Paul Erdős was one of the most famous mathematicians of the 20th century. He left a large number of unsolved mathematical conjectures, collectively known as "Erdős problems". Among them, the problem of the lower limit of the original set - that is, no number in a set can be evenly divided by another number - has a history of about 60 years since it was proposed.

Stanford University mathematician Jared Lichtman proved Erdős's conjecture about the upper limit of the maximum value of 1.6 in his 2022 doctoral thesis, but was also stuck on the proof of the minimum value (the lower limit is 1). Many top mathematicians, including Lichtman, failed to overcome this difficulty.

Liam Price originally asked this question to ChatGPT during his occasional "vibe mathing" habit. His usual approach is to visit erdosproblems.com, pick an open problem at random, and see what results the AI can give. This time, he didn't expect there would be a real breakthrough.

What's even more surprising is that Price's partner Kevin Barreto - a sophomore mathematics student at Cambridge University - reviewed it and found that it was not just an answer, but a completely new proof method. Barreto immediately contacted relevant experts, and the news quickly reached Professor Terence Tao.

Dimensions	Details
Question Type	Lower bound guess for Primitive Sets
Age in question	About 60 years
Previous Triers	Many top mathematicians, including Fields Medal winners
Solution source	GPT-5.4 Pro single prompt generation
Level of Innovation	Brand new methods - directions that humans have never thought of
Review and Confirmation	Confirmed by Professor Terence Tao
Publishing platform	Scientific American (top media in the scientific community)

Adaptation suggestions

This incident has several important implications for AI practitioners and content creators:

1. AI is eliminating professional barriers

If you think "AI can only do ordinary jobs" - please think again. A person without a degree in mathematics, using a $200/month ChatGPT Pro subscription, has done what top academics cannot. This is consistent with the core view of waytoclawearn.com: AI tools are the ability amplifiers of modern people.

2. "Vibe Coding" is upgraded to "Vibe Mathing

Price calls his activity "vibe mathing"—casual questioning and unrestricted AI exploration. This is in line with the popular "vibe coding" in the field of programming: you are not replacing experts, but using AI as a thinking partner to discover new possibilities.

3. The value difference between ChatGPT Pro and the free version

Price didn't get a breakthrough when he first tried using free ChatGPT. He got a breakthrough solution after switching to GPT-5.4 Pro. The paid version model has stronger reasoning capabilities and has obvious advantages when dealing with tasks that require deep thinking.

4. Specific action suggestions

Try using ChatGPT Pro/GPT-5 for complex reasoning tasks, don’t just limit it to daily Q&A
Dare to throw "impossible" problems to AI - you may suddenly get a breakthrough
Apply this approach across domains: code development, automated workflows, market analysis, etc.

Tool entry

In this case, the value of tools is clearly demonstrated. The tool name appearing in the text can directly trigger the tool's floating information card on waytoclawearn.com: ChatGPT, OpenAI, GPT-5. If you are building your own AI automation workflow, you can refer to the practical tutorials on the site.

GPT-5 Pro

Reference sources

Scientific American: "An amateur just solved a 60-year-old math problem—by asking AI" (April 24, 2026)
Hacker News discussion: 755 points / 539 comments
erdosproblems.com (Erdős problems online platform)
Confirmed comments by Professor Terence Tao (UCLA)

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