AI and Math: Why Human Communities Still Matter to Mathematical Theory

Summary

The essay responds to arguments about the future of mathematical research after AI, focusing on the claim that artificial intelligence cannot yet develop mathematical theory. It frames scientific and mathematical communities as collective intelligences whose shared language lets theories gain acceptance, persist, and support further discoveries. Current large language models can acquire, use, and teach language with superhuman ability, but the author argues that they lack the persistence, life experience, identity, and community membership needed to become durable nodes in this larger network. Even if AI eventually produces new theories, those theories would still need acceptance by human communities unless AI systems could form persistent communities of their own. The author suggests that mathematicians may remain essential and should continue to be supported as full-time researchers, while LLMs could make mathematical communities more accessible. The essay also considers whether an “AlphaGo Zero of mathematics,” trained by retracing mathematical development through self-play, could produce comparable theory-building capabilities. The author is skeptical that this proposal is coherent or feasible, and leaves the question open.