In mid-May, OpenAI revealed that one of its internal AI models had successfully disproven the Erdős unit distance conjecture, a longstanding enigma in discrete geometry that has puzzled mathematicians for nearly 80 years.
Following this announcement, OpenAI granted select mathematicians early access to the findings and shared their reactions. Tim Gowers, a recipient of the Fields Medal—the highest accolade in mathematics—expressed that “there is no doubt that the solution to the unit-distance problem is a milestone in AI mathematics.”
Professor Daniel Litt from the University of Toronto remarked that “this represents the first instance of an AI producing a result that is thrilling in its own right, rather than merely serving as a preliminary indicator.”
This development could be seen as a significant breakthrough in AI's ability to solve major unsolved mathematical problems. Nevertheless, it should be noted that this does not represent a complete departure from AI’s previous advancements in mathematics.
Just three years ago, large language models (LLMs) faced difficulties even with simple arithmetic tasks. However, by last year, they began to excel in high school-level mathematics competitions.
During my participation in the Joint Mathematics Meetings—the largest global gathering for mathematicians—in January, I observed that while AI systems were beginning to contribute to mathematical research, their roles were still limited. It required considerable human effort to refine AI outputs into verifiable theorems.
OpenAI’s recent findings signify a progression in this journey. The AI model skillfully synthesized existing concepts from various mathematical domains to construct a comprehensive proof. However, it did not introduce any fundamentally new methodologies. Subsequently, human mathematicians have taken the initiative to polish and expand upon the initial result.
This suggests a future where human mathematicians and AI systems may work in tandem. AIs can draw on a vast repository of historical knowledge and demonstrate an impressive capacity for tackling tedious proof methods that may seem unpromising. Conversely, human thinkers possess the ability to engage deeply with specific problems and pose more compelling questions.
