Grant Sanderson argues that mathematics should formally recognize and reward "motivated explanations" - expositions that prioritize intuition, historical context, and the sense of how one would discover an idea - on par with the traditional credit given for proving theorems. Motivated explanations place definitions after the problem is established, allow provisional or flawed heuristics refined through narrative ("discovery fiction"), and aim to explain why a theorem is the right question and how its ideas fit into broader practice. Unlike proofs, which are binary and machine-checkable, motivated explanations are subjective but verifiable enough to be evaluated by whether key ideas feel discoverable and where they come from. Elevating this genre responds to the risk that proof-generating machines will devalue human contributions if exposition and understanding remain second-class.
Concrete precedents and proposals illustrate the case: the explanatory essays in Part IV of the Princeton Companion, Timothy Gowers’ decision to prioritize exposition, Bill Thurston’s advocacy for non-credit-producing work (including influential visualizations like sphere eversion videos), and Timothy Chow’s concept of "open exposition problems." A rubric and institutional incentives should be developed to treat major exposition problems like research problems, with leaders selecting important unsolved exposition targets. Recent instances of AI-assisted proofs, exemplified by a GPT-5.4-aided solution to an Erdős problem, underscore the urgency of prioritizing human-understanding tasks that machines cannot substitute.
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