In a development that has captured the attention of mathematicians worldwide, a 23-year-old enthusiast named Liam Price has used the AI chatbot ChatGPT to propose a solution to one of the famously difficult Erdős problems, a set of conjectures posed by the late Hungarian mathematician Paul Erdős. The proposed proof, posted on erdosproblems.com, has been examined by leading experts who say it is legitimate, marking a rare instance where AI has contributed a genuinely novel mathematical insight.
The Erdős problems, named after the prolific mathematician who died in 1996, have stumped researchers for over sixty years. Price, who holds no advanced degree in mathematics, said he simply prompted GPT-5.4 for an answer. While many previous AI-generated attempts at these problems have been dismissed, this one stood out because it took an unexpected route that humans had overlooked.
Terence Tao, a mathematician at the University of California, Los Angeles, who has become a key figure in evaluating AI's role in mathematics, told Scientific American that the solution is different from typical AI outputs. He noted that everyone who had previously worked on the problem started with a standard sequence of moves, but the AI applied a well-known formula that no one had thought to use in this context. Tao, who maintains a database of AI-assisted Erdős solutions, said that in most cases the AI either resurrected an existing but obscure proof or produced something that was not quite correct.
Human Expertise Still Essential
Despite the AI's contribution, the final proof required human intervention. Jared Lichtman, a mathematician at Stanford University whose doctoral thesis focused on one of Erdős's conjectures, told Scientific American that the raw output from ChatGPT was quite poor and needed an expert to sift through and understand what it was trying to say. This collaboration between machine and human expertise highlights a new dynamic in mathematical research.
Tao expressed enthusiasm about the achievement, saying, "We have discovered a new way to think about large numbers and their anatomy. It's a nice achievement. I think the jury is still out on the long-term significance." His cautious optimism reflects the broader sentiment in the mathematical community, which is intrigued but wary of overhyping AI's capabilities.
The breakthrough comes with a cautionary tale. In October, an OpenAI vice president, Kevin Weil, prematurely celebrated a ChatGPT solution to another Erdős problem, only to retract his claim after it was revealed that the AI had drawn from an existing solution. The incident underscores the need for rigorous verification before declaring AI-driven breakthroughs.
This latest success, however, suggests that AI can sometimes break free from the "flawed hivemind" of human approaches, offering a fresh perspective that might otherwise be missed. As researchers continue to explore the potential of AI in mathematics, the collaboration between human intuition and machine pattern recognition could lead to further discoveries, though experts advise caution and careful scrutiny of every claim.
A 23-year-old without an advanced math degree used ChatGPT to propose a solution to a long-standing Erdős problem, which experts like Terence Tao have verified as a genuine breakthrough. The AI's unconventional approach, though requiring human refinement, suggests new possibilities for machine-assisted mathematical discovery.
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