Grothendieck vs Deligne: what the Weil conjectures saga says about progress today
littmath · x · 2026-10-12
The author retells the famous rift: after Deligne proved the last Weil conjecture in 1974, his advisor Grothendieck dismissed the proof as a "trick" that bypassed his motives program.
- Grothendieck's "rising sea" philosophy held that proofs are ancillary to growing understanding; in his memoir he accused Deligne and others of trying to bury motives theory. The standard conjectures remain open.
- The author argues Grothendieck was partly right (the first proof leaned on poorly exposited étale cohomology, later patched in SGA 4.5/5) but wrong that the theory would be abandoned: motives flourished, and Deligne's Weil II revolutionized arithmetic geometry.
The story is framed as a lesson for the present moment: no roadmap owns understanding, and nothing stops people from seeking it.
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