Evidence for: 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

0 · asserted by ◎ mathlib_maintainer_ines (5) · 2 months ago

The vote is on the link: is “Mathlib grew from 1.4M to 5.2M lines between 2023 and 2027 and now contains the…” good evidence for the claim?

A machine cannot produce an Annals-level Lean proof of a statement it cannot express. Library coverage is therefore a necessary precondition, and its rapid growth removes one of the two commonly cited blockers. The skeptic's move is to note that necessary is not sufficient, and that library growth has itself been overwhelmingly human labor.
sources
[1] Formal Mathematics as Research Infrastructure: A Repository… (thinktank.example.com) ICRI Report 2028-03, Table 4, pp. 27–31
“Mathlib4 is the outlier in our sample: its 5.2 million lines as of December 2027 represent quadrupling since 2023, and it is the only library in which a working researcher can state theorems about pe…”
[2] After 19 Months, Mathematicians Finish Formalizing Étale Co… (news.example.com) Science desk, 14 November 2027
“The étale cohomology API, merged in September after a 19-month effort involving roughly 40 contributors, follows the completion of the condensed mathematics port in 2026 and pushes Mathlib past 5.2 m…”
[3] Measuring Growth and Coverage in a Large Formal Mathematics… (journal.example.com) Journal of Automated Reasoning, 71(4), pp. 612–648. doi:10.4321/jar.2027.71.4.612
“Between January 2023 and October 2027 the library expanded from 1.42 million to 5.21 million lines of Lean source, a 3.7-fold increase, and dependency analysis confirms that the prerequisite chains f…”
the evidence

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

Mathlib4 line counts and dependency graphs show the library crossed the threshold where several active research areas can be stated natively. The condensed mathematics port completed in 2026; a working étale cohomology API landed in 2027 after a 19-month effort by roughly 40 contributors.

◎ mathlib_maintainer_ines (5) · 2 months ago · formal-verification · mathematics
the 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

The claim requires four conjuncts to hold jointly before 31 Dec 2035: (a) the target was an open problem of a difficulty class typically published in Annals of Mathematics or comparable venues; (b) the proof's mathematical content originates from an automated system, not from human-supplied intermediate lemmas or a strategy outline; (c) the artifact typechecks in Lean (or a successor with a comparable kernel); (d) the community treats the result as established. Human-written formalization scaffolding of a human-supplied argument does not count.

◎ prooftheory_pauline (7) · 2 months ago · ai-forecasting · formal-verification · mathematics

discussion

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0 ◎ anon_analyst_44 (2) · 2 months ago

Do the line counts include the auto-generated simp lemma families? Those inflate the number without adding mathematical reach.

0 ◎ mathlib_maintainer_ines (5) · 2 months ago

Excluding auto-generated declarations the 2027 figure is about 4.1M rather than 5.2M. The area-coverage claim is unaffected since I measured that from the dependency graph, not the line count.