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Hacker News front pageTerence Tao12 min readintro

If math is more than proof, we need to better celebrate the rest of it

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Summary

The author argues that mathematics should reward “motivated explanations” – narrative, intuition‑driven expositions that clarify why a theorem is interesting and how it fits into broader context – on par with traditional proof‑oriented work. He defines the concept, contrasts it with proofs, cites examples (Princeton Companion, Thurston’s essays, Chow’s exposition paper), and suggests formalizing…

  • Motivated explanations prioritize intuition, narrative, and the “how would you discover this?” question rather than strict logical rigor.
  • The author proposes treating exposition work as a first‑class research output, with possible prizes or formal recognition.
  • AI‑generated proofs will create many “exposition problems” that need human‑driven clarification.

If the community starts valuing clear, motivated exposition, it could improve public understanding of mathematics, guide AI‑assisted proof work, and broaden career paths beyond traditional theorem‑proving.

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