In a recent guest post, mathematician Terence Tao and educator Grant Sanderson propose a shift in how the mathematics community assigns academic credit. They argue that while solving problems and generating proofs have historically served as the primary metrics for success, these activities are merely proxies for the true goal of mathematics: advancing human understanding. As automated systems become increasingly capable of generating proofs, the authors suggest that the field must better celebrate 'motivated explanations'—work that answers the question of how one would arrive at a mathematical insight, rather than simply confirming its validity. The authors define a motivated explanation as one where definitions are introduced only after a problem is clearly established, and where the narrative allows for relatable, iterative discovery. This approach contrasts with traditional proofs, which often begin with abstract definitions and proceed through necessary logical implications. By elevating the status of such expository work, the authors believe the community can better communicate the value of mathematical research to the public and correct the misconception that proof-generating machines render human mathematicians obsolete. To implement this, they suggest practical changes, such as PhD programs emphasizing the presentation of clear, motivated solutions over rote problem-solving. They point to existing exemplars, such as the 'Princeton Companion to Mathematics' and the work of the late Bill Thurston, as models for this type of contribution. The authors also highlight recent developments in number theory, where AI-assisted proofs of problems like Erdős Problem 1196 were only fully integrated into the field after human researchers clarified the underlying ideas, demonstrating that the true value often lies in the subsequent contextualization rather than the initial proof itself.
The article highlights the late Bill Thurston as an exemplar of how mathematicians can contribute to the field through deep conceptual clarity and motivated explanations rather than just formal proofs.