Mathematics in the Age of AI
This presentation examines how advanced AI systems challenge mathematics not at the level of formal correctness, but at the level of institutional values and collective understanding. By decomposing problem-solving into five distinct stages—from proof generation through canonicalization—the analysis reveals that AI may create proof abundance while amplifying bottlenecks in verification, exposition, peer review, and theory integration. The talk argues that mathematical institutions must explicitly articulate their goals and shift recognition from proof generation toward the expert work of digesting and canonicalizing mathematical knowledge.Script
Russell's paradox forced mathematics to make its foundations explicit. Now AI is forcing mathematics to make its values explicit, and the crisis is not about truth but about what the community actually rewards and recognizes.
For centuries, mathematics optimized visible proxies like publication counts and solved problems because those metrics reliably tracked a bundle of deeper goals: understanding, technique development, community building, and aesthetic value. That alignment is breaking.
The paper decomposes problem-solving into five stages: proof generation, verification, exposition, publication, and canonicalization. Under proof abundance, the bottleneck shifts from the first stage to the last four, where expert attention converts isolated derivations into collective mathematical knowledge.
A formally correct proof is not the same as an understood proof. The paper argues that mathematical exposition should preserve the structure of difficulty, because the friction of working through a proof often transmits tacit expertise and reveals where the actual intellectual obstacles lie.
AI systems depend on canonicalized human mathematics as training data, but they do not inherently produce canonicalization. This creates a structural asymmetry: AI generates candidate proofs, but the definitive theory that makes future AI possible still requires human mathematical labor.
The central recommendation is explicit: reduce cultural emphasis on proof generation and priority, and increase recognition for exposition, attribution, refereeing, and canonicalization. Visit EmergentMind.com to explore this paper in depth and create your own video presentations.
