Amateur armed with ChatGPT solves an Erdős problem

A 23-year-old amateur mathematician has solved a 60-year-old problem originally posed by Paul Erdős, using the artificial intelligence tool ChatGPT Pro. The breakthrough came after a single prompt to GPT-5.4 Pro, which produced a novel solution method that had eluded professional mathematicians for decades. The problem, related to “primitive sets” of whole numbers—sets where no element divides another—had resisted human attempts but was cracked by the AI-assisted approach, marking a significant milestone in the use of large language models in mathematical research. The problem involves Erdős’s concept of primitive sets, which generalize the idea of prime numbers to collections of integers with no divisibility relations among them. Erdős introduced a measure known as the Erdős sum, a value assigned to any primitive set, and conjectured that the maximum sum corresponds to the set of all prime numbers. While some aspects of this conjecture have been proven, the specific problem solved by the AI had remained open despite efforts by leading mathematicians. Experts note that the AI’s solution employed a method not previously considered by humans, suggesting a fresh perspective that could have broader implications for number theory. Prominent mathematicians, including Fields Medalist Terence Tao, have acknowledged the significance of this development. Tao pointed out that the problem was likely simpler than initially thought but had been hindered by a collective mental block among researchers. The AI’s ability to bypass this block and generate an original approach highlights the evolving role of artificial intelligence in advancing mathematical discovery. While earlier AI successes on Erdős problems were sometimes criticized for lacking originality or significance, this new result stands out for its novelty and potential applicability. This achievement underscores the growing impact of AI tools like ChatGPT in tackling complex scientific challenges, even by individuals without formal advanced training. It raises important questions about the future collaboration between human intuition and machine-generated insights in mathematics and other disciplines. The solution has been shared publicly on a website dedicated to Erdős problems, inviting further scrutiny and exploration by the mathematical community.