In a remarkable turn of events, an OpenAI model has solved a famous math problem that had stumped humans for over eight decades. This achievement, while impressive, is not a radical departure from the trajectory of AI progress in mathematics. Three years ago, Large Language Models (LLMs) were struggling with basic arithmetic, and only recently started acing high school mathematics competitions. The breakthrough in question involves the Erdös unit distance conjecture, a problem in discrete geometry that had eluded human mathematicians for 80 years. OpenAI's model cleverly applied existing mathematical ideas to create a full proof, but it didn't introduce any genuinely new techniques. This result points to a future where human mathematicians and AI models work together, with AIs having a broader knowledge of past work and more willingness to explore tedious proof strategies, while humans excel at deeper thinking and asking more interesting questions. However, the role of human mathematicians may not last, as AI systems continue to improve rapidly. The author reflects on the dynamic between humans and AI in mathematics, highlighting the strengths of both. While AI models can tackle complex problems and explore a wide range of mathematical ideas, humans are still essential for choosing questions and developing new techniques. The article concludes by speculating on the future of AI in mathematics, suggesting that the collaboration between humans and AI will likely continue to evolve, with AI systems becoming more autonomous and capable of making significant contributions to the field.
