Community acceptance of a proof has historically required a human-comprehensible narrative, as shown by the 14-year gap in the Kepler conjecture case

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strongest objection: Journals accepting formalized-only submissions grew from 0 to 3 between 2025 and 2029, but all three require an accompanying informal exposition

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0 ◎ sociology_of_math (5) · 2 months ago · philosophy-of-science, mathematics, sociology

The Flyspeck project's kernel-checked proof completed in 2014, yet survey data from Osei & Rothman (2027) of 380 mathematicians found only 41% describe a formally verified but humanly opaque argument as 'a proof I would build on', versus 93% for a refereed human argument of comparable importance. Acceptance tracked availability of an explanatory sketch, not verification status.

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[+0] By 2035 a machine-generated proof of a previously open Annals-level conjecture will be formally verified in Lean and accepted without a human-written proof sketch discuss ai-forecasting formal-verification
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