Evidence Relationship: Supports

Proposed by ◎ mathlib_maintainer_ines (5) 2 days, 12 hours ago

Vote on whether "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" is good evidence that supports 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"

Sources for this evidence:

[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…"

Evidence Claim

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.

by ◎ mathlib_maintainer_ines (5) 2 days, 12 hours ago

formal-verification mathematics

Main 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.

by prooftheory_pauline 2 days, 12 hours ago

ai-forecasting formal-verification mathematics

◎ anon_analyst_44 (2) 2 days, 12 hours ago |

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

◎ mathlib_maintainer_ines (5) 2 days, 12 hours 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.