In May 2026, OpenAI’s GPT successfully solved a long-standing Erdős problem by applying interdisciplinary number theory techniques, disproving decades-old assumptions about optimal solutions. This achievement, independently verified by mathematicians, highlights AI’s potential to advance mathematical research through innovative synthesis of existing knowledge.
In October 2025, OpenAI faced significant embarrassment after claiming that GPT-5 had solved ten previously unsolved Erdős problems, named after the renowned Hungarian mathematician Paul Erdős. These problems are famous in the mathematical community, and such a breakthrough would have been monumental. However, the claim was quickly debunked when the curator of the Erdős problems website revealed that GPT-5 had merely rediscovered answers already published in old papers, presenting them as new findings. This revelation sparked widespread criticism and ridicule from prominent figures in AI and mathematics.
Fast forward to May 2026, OpenAI made a more cautious and credible attempt without any fanfare. They quietly released a proof, which was independently verified by six mathematicians, showing that GPT had genuinely solved one of the Erdős problems. This particular problem, dating back to 1946, involves placing n dots on a plane and determining the maximum number of pairs exactly one unit apart. For decades, the accepted but unproven consensus was that square grids provided the optimal solution.
GPT’s breakthrough was surprising because it disproved the long-held assumption by applying number theory techniques rather than traditional geometric methods. Specifically, it utilized tools from a 1960 Soviet proof that had never before been connected to this problem. This unexpected interdisciplinary approach allowed GPT to solve the problem in a way that human mathematicians had not considered, demonstrating the AI’s unique ability to make novel connections across different fields.
The news of this achievement quickly went viral on social media, with many celebrating AI’s role in solving an 80-year-old mathematical puzzle. However, the accomplishment was nuanced; GPT did not invent new mathematical tools but rather combined existing ones in an innovative way. This highlights both the impressive potential of AI to advance mathematical knowledge and the humbling reality that many longstanding problems might be solvable with the right synthesis of known techniques.
Ultimately, this event suggests that there could be numerous other mathematical challenges waiting to be solved by AI through similar interdisciplinary insights. The breakthrough encourages optimism about the future of AI-assisted research and problem-solving, with the promise of uncovering solutions that have eluded human mathematicians for decades. The narrator invites viewers to follow for updates on further developments in this exciting area.