← back to claim 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

evidence graph

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
supports (2)
[+0] Mathlib grew from 1.4M to 5.2M lines between 2023 and 2027 and now contains the prerequisites for perfectoid spaces, condensed mathematics, and étale cohomology discuss [i]
[+0] Machine-authored contributions accounted for 31% of merged Mathlib pull requests in 2027, up from under 1% in 2024 discuss [i] software-engineering
[+0] Autoformalization success on undergraduate competition corpora rose from 8% to 61% between 2022 and 2025 on the miniF2F-Lean4 benchmark discuss [i] machine-learning
[+0] Proof length distribution on solved miniF2F problems is bounded above by 40 tactic steps, with a 96th-percentile of 22 discuss [i]
[+0] Held-out contamination audit found miniF2F-Lean4 gains persist at 54% on 300 freshly authored problems never posted online discuss [i]
[+0] Independent re-evaluation by the Zurich formal methods group reproduced 51.8% on the held-out set with a clean-room rebuild of Kestrel-7 discuss [i] reproducibility
opposes (3)
[+0] Kernel-level trust in Lean is illusory because every large formalization to date has relied on axioms or porting steps outside the verified core discuss [i] logic
[+0] Community acceptance of a proof has historically required a human-comprehensible narrative, as shown by the 14-year gap in the Kepler conjecture case discuss [i] philosophy-of-science sociology
[+0] Journals accepting formalized-only submissions grew from 0 to 3 between 2025 and 2029, but all three require an accompanying informal exposition discuss [i] publishing
[+0] No automated system has produced a proof requiring a definition absent from its training library, across 11 documented research-level attempts discuss [i]
[+0] The 2028 survey's six 'requires new construction' problems were rated by referees who knew the eventual human solution in four cases discuss [i] research-methods
[+0] Inter-rater agreement on 'requires new mathematical machinery' judgments is κ = 0.31 among 22 research mathematicians shown 40 solved problems discuss [i]
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