Amateur Mathematician Solves 60-Year-Old Problem Using ChatGPT
By Joseph Howlett | Scientific American | April 24, 2026
Liam Price is 23. He is an amateur with no advanced math training. He solved a math problem that has confused experts for 60 years. His tool was ChatGPT Pro, which uses OpenAI’s GPT-5.4 model. In this work, each word links closely with its neighbor so the ideas stay clear.
Cracking a Long-Standing Mathematical Puzzle
Price worked on a problem posed by Paul Erdős. Erdős asked about "primitive sets." In these sets, no number divides another. This idea extends prime numbers. Primes only divide themselves. Erdős also made the “Erdős sum.” This sum gives a score to each set, and he guessed its limits.
Some parts of Erdős’s guesses have been proved. One stubborn question stayed. It asks if primitive sets made of large numbers have an Erdős sum that is always at least one. As the numbers grow, the sum should come close to one. Even top mathematicians, like Jared Lichtman from Stanford University, had trouble here. Lichtman solved one part in 2022 but could not finish this piece.
An Unconventional Approach Via AI
Price did not know the history behind the problem. One Monday, he put the problem into ChatGPT. He wanted to see what the AI would say. In one prompt, the AI produced a solution that looked valid.
Price then worked with Kevin Barreto from the University of Cambridge. Barreto is an undergraduate in mathematics. He quickly saw that the AI’s method was new and important. Soon, mathematicians took notice of the solution.
Terence Tao from UCLA watched these AI efforts. He pointed out that human experts usually use the same steps. Instead, ChatGPT used a new formula from related fields. Tao said, “The AI took a different path with familiar ideas, but it connected them in a novel way.” The AI’s first draft needed human touch to refine the proof. Still, it gave a fresh and elegant view of the problem.
New Insights and Future Potential
Experts now see more than just one solution. Lichtman said the proof shows that all Erdős problems share a hidden link. Tao called the work “a new way to think about large numbers and their structure.” He sees further uses for this idea in math.
Even though the AI gave the first answer, humans helped check and polish the work. Their input shows that AI works best as a partner, not a replacement.
The Rise of AI in Mathematical Discovery
This work comes as more people ask if AI can solve problems like Erdős’s. Earlier, AI solutions were often unoriginal or reused old methods. This new solution stands out. The AI found a new path that no human had tried before.
This mix of humans and AI is part of a growing trend called “vibe-mathing.” In this work, researchers ask language models to help find new ideas in math.
Looking Ahead
For now, the math community feels both hope and caution. As Tao noted, "The jury is still out on the long-term significance." They hope that AI ideas will soon help solve other old problems.
Price’s story shows that AI can help anyone—from amateurs to experts—join cutting-edge research. Scientific American will keep sharing these bold moments where human ideas and technology meet.
Joseph Howlett is a staff reporter at Scientific American. He covers physics, math, and astronomy. He has a Ph.D. in particle physics from Columbia University and once wrote for Quanta Magazine.
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