A long-standing mathematical puzzle linked to the work of Paul Erdős has reportedly been solved with the help of ChatGPT, bringing fresh attention to how artificial intelligence is beginning to intersect with advanced mathematics.
What is the Erdős primitive set problem and why is it so difficult
The puzzle originates from mathematician Paul Erdős, whose work shaped much of modern number theory. The specific ‘primitive set’ problem deals with sets of integers where no number divides another. While the concept sounds simple, the deeper mathematical structure becomes extremely complex when scaled. For decades, researchers have attempted to prove or refine key properties related to these sets.
Experts reportedly revisited the problem multiple times over the years. Each attempt followed a similar mathematical pathway. That repetition may have limited progress. It appears that most approaches stayed within established reasoning patterns, even when those patterns did not lead to a solution. The problem became one of those long-standing mathematical questions that sits in journals for years without resolution. Not forgotten, but not solved either.
How ChatGPT helped unlock a new approach to the Erdős primitive set problem
The recent progress came when Liam Price, an amateur mathematician, used ChatGPT-5.4 Pro during an extended working session lasting around an hour and twenty minutes. Instead of introducing a new formula, the AI model reportedly applied a well-known mathematical tool in a different context. That shift in application became the key point. The same formula had existed for years, but had not been used in this specific way for the Erdős problem.
ChatGPT’s role, according to reports, was not to “invent” mathematics. It generated multiple lines of reasoning quickly and explored combinations that a human might not naturally prioritise. This process led to an unexpected connection between known mathematical principles. The solution appears to rest on reinterpreting familiar concepts rather than creating new ones. That detail has become central to how researchers are evaluating the outcome.
Terence Tao’s view on early assumptions in the Erdős primitive set problem
Mathematician Terence Tao reportedly reviewed the solution and offered cautious observations. He suggested that earlier researchers may have taken a “wrong turn” at an early stage of analysis. According to his comments, the difficulty may not have been due to complexity alone. It might also have been a shared assumption among mathematicians about how the problem should be approached. He indicated that most human attempts followed a similar logical path. That path seemed reasonable, but may have narrowed the range of possible solutions too early.
In contrast, ChatGPT explored alternative routes without being influenced by established academic habits. That difference in approach is being discussed as a possible reason for the breakthrough.
What this means for mathematical research
The development has raised questions about the role of artificial intelligence in advanced research. Experts suggest it should not be seen as replacing mathematicians. Instead, it may function as a tool for exploring large numbers of possibilities quickly. The result also highlights how long-standing problems can sometimes persist not because they are unsolvable, but because the same methods are repeatedly used. There is no suggestion that ChatGPT independently solved the problem in a traditional sense. Rather, it assisted in identifying a direction that had been previously overlooked.
The news was reported by the TOI Tech Desk, a dedicated team of journalists committed to delivering the latest and most relevant news from the world of technology to readers of The Times of India. The coverage spans gadget launches, reviews, trends, in-depth analysis, exclusive reports, and breaking stories that impact technology and the digital universe, including how-tos, AI, cybersecurity, personal gadgets, and platforms like WhatsApp, Instagram, and Facebook.
