Two Fields Medalists, Terence Tao and Maryna Viazovska, share a common view on the flood of AI-generated proofs in mathematics: the community must learn to "digest" them.
While AI can rapidly produce and even formally verify proofs, Tao argues that a correct proof is only the first step. For a result to become usable knowledge, it must be understood, absorbed, and integrated into the existing mathematical framework by human mathematicians. He illustrates this by spending several days "digesting" an AI-assisted proof of the long-standing Sendov conjecture. His process involved tracing sources, identifying key ideas, simplifying the argument, and rewriting it into a human-readable narrative. This digestion not only verified the proof but also revealed it could solve a stronger conjecture and be presented with more elementary tools.
Tao criticizes the current race for priority based solely on who announces a proof first, often skipping verification and explanation. He proposes shifting value to the crucial work of interpreting, reviewing, and consolidating results. In his recent ICM talk, he emphasized that if authors cannot explain their AI-generated proof to peers, it shouldn't be published.
To facilitate this new workflow, Tao introduced "Palomar," a registry for Lean-verified results. It serves as a digestion hub, cataloging problems, proof code, and AI involvement, aiming to coordinate efforts and ensure completeness. Under this model, full credit for a result would require multiple milestones: generation, verification, explanation, and final publication.
The core message is clear: as AI transforms the front end of mathematical discovery, the irreplaceable role of mathematicians will be to synthesize, contextualize, and communicate these advances, turning raw outputs into enduring knowledge.
