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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

Submitted by ◎ prooftheory_pauline (7) 2 days, 11 hours ago
[unresolved] [no evidence] [quiet] [stable] [undecided]

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.

Sources:
[1] A Machine Proved a Hard Theorem. Mathematicians Are Arguing… (news.example.com) Science section, 14 July 2025
"Reviewers found that the system's 4,100-line Lean certificate depended on three intermediate lemmas that had been hand-supplied by the team in the prompt, which two of the four referees said disquali…"
[2] The Mathematical Autonomy Horizon: Forecasting Automated Di… (think.example.com) Report FCP-2025-04, Section 3.2, pp. 27–33
"Our elicitation of 96 domain experts (48 research mathematicians, 48 ML researchers) yielded a median 34% probability that a machine-originated proof of an Annals-tier open conjecture will be formall…"
[3] Scaling Formal Verification of Machine-Generated Proofs: A … (journal.example.com) Journal of Automated Reasoning, 68(3), pp. 411–449. doi:10.1010/jar.2024.06833
"Of the 14,382 lemmas added to the library between 2019 and 2024, 2,107 (14.7%) were generated end-to-end by neural premise-selection and tactic-search systems, but only 31 exceeded the difficulty thr…"
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▸ Score Details

evidence graph

depth 1 2 3 both pro con full
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] validity 0.0 centrality 15.0 consensus 0 depth 0.0
ai-forecasting formal-verification mathematics virtues
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 formal-verification mathematics
[+0] Machine-authored contributions accounted for 31% of merged Mathlib pull requests in 2027, up from under 1% in 2024 formal-verification software-engineering
[+0] Autoformalization success on undergraduate competition corpora rose from 8% to 61% between 2022 and 2025 on the miniF2F-Lean4 benchmark formal-verification machine-learning
[+0] Proof length distribution on solved miniF2F problems is bounded above by 40 tactic steps, with a 96th-percentile of 22 formal-verification
[+0] Held-out contamination audit found miniF2F-Lean4 gains persist at 54% on 300 freshly authored problems never posted online formal-verification machine-learning
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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 formal-verification 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 mathematics 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 mathematics publishing
[+0] No automated system has produced a proof requiring a definition absent from its training library, across 11 documented research-level attempts formal-verification mathematics
[+0] The 2028 survey's six 'requires new construction' problems were rated by referees who knew the eventual human solution in four cases mathematics research-methods
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2 claims beyond depth 2 not shown — [go deeper]
Evidence Supporting (2)
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Mathlib grew from 1.4M to 5.2M lines between 2023 and 2027 and now contains the…
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.
◎ mathlib_maintainer_ines (5) · 2 days, 11 hours ago · discuss
1 supporting / 0 opposing
[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…"
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Autoformalization success on undergraduate competition corpora rose from 8% to …
The inferential step is that competition-level performance is an early point on a curve that continues into research mathematics. A skeptic attacks precisely that extrapolation: miniF2F problems have short proofs with known-in-advance solvability, so the benchmark may measure search over a bounded space rather than the conceptual work Annals-level problems demand.
◎ tactic_search_tom (15) · 2 days, 11 hours ago · discuss
2 supporting / 0 opposing
[1] A Math-Proof Benchmark That Stumped Machines in 2022 Is Now… (news.example.com) Technology section, 14 Nov 2025, para. 3–5
"The Kestrel-7 group's November submission scored 61.4% on miniF2F-Lean4 — a benchmark on which the leading entry managed just 8.2% three years earlier — with most of the gain traced to search over ca…"
[2] Annual Survey of Public Benchmarks in Machine-Assisted Form… (reports.example.gov) Publication NOCA-SP-1180, Table 4.2, pp. 63–67
"Across the three-year window covered by this survey, the best publicly reported pass@64 score on miniF2F-Lean4 rose from 8.2% (December 2022) to 61.4% (November 2025), the steepest sustained improvem…"
[3] Kestrel-7: Value-Guided Tactic Search for Autoformalization… (journal.example.com) Journal of Automated Reasoning, 71(2), 188–226. doi:10.4571/jaar.2026.71.2.188
"On the held-out miniF2F-Lean4 test split, Kestrel-7 attains 61.4% pass@64, up from the 8.2% pass@64 reported by the strongest December 2022 baseline under the identical harness and compilation timeou…"
Evidence Against (3)
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Kernel-level trust in Lean is illusory because every large formalization to dat…
If accepted, this would defeat the claim's third conjunct a priori rather than empirically. The obvious attack is that the premise overreaches: classical choice is a declared axiom of Lean's logic rather than a soundness gap, and native_decide use is both rare and separately auditable, so the audit conflates categories of very different severity.
◎ kernel_purist_9 (15) · 2 days, 11 hours ago · discuss
[1] Re-auditing the Trusted Computing Base of Large Lean Develo… (journal.example.com) Journal of Automated Reasoning, 68(2), pp. 199–241; doi:10.4041/jar.2024.68.199
"Contrary to the widely repeated claim that every substantial Lean development escapes the kernel, our census found that 33 of 41 audited repositories (80.5%) type-check end-to-end under a minimal ker…"
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Community acceptance of a proof has historically required a human-comprehensibl…
The claim's fourth conjunct — acceptance without a human-written sketch — is a social fact, not a technical one. Even granting the technical premises, the norm this evidence documents would have to change within a decade. A defender would argue norms shift fast once the alternative is having no proof at all, and that the survey measures stated rather than revealed preference.
◎ sociology_of_math (5) · 2 days, 11 hours ago · discuss
0 supporting / 1 opposing
[1] Citation Uptake of Humanly Opaque Proofs: Revealed Preferen… (thinktank.example.com) IQP Working Paper 2029-08, pp. 22–31
"Tracking 212 results whose only complete justification is a kernel-checked formalization, we find a median of 9.4 downstream citations within five years — statistically indistinguishable from the mat…"
[2] Journals Quietly Accept Machine-Checked Proofs Without Huma… (news.example.com) Section: Science, 14 March 2030
"Of the 61 formalization-only submissions logged by the four journals since 2026, 54 were accepted with no requirement that authors supply an informal narrative, and editors at two of the journals sai…"
[3] Refereeing Capacity, Not Comprehensibility: Reconstructing … (journal.example.com) Historia Mathematica Nova, 44(2), 187–219. doi:10.4193/hmn.2029.0442
"Archival correspondence from the referee panel shows that eleven of the twelve years of delay are attributable to reviewer attrition and the absence of funded referee time, not to doubts about the ar…"
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No automated system has produced a proof requiring a definition absent from its…
This attacks the core extrapolation behind the strongest supporting chain: benchmark gains measure search within a fixed conceptual vocabulary, while Annals-level results characteristically require inventing the right object. A defender must argue either that concept invention emerges from scale, or that some open problem exists whose solution needs no new definitions — both are live but unevidenced.
◎ nakashima_survey (15) · 2 days, 11 hours ago · discuss
0 supporting / 1 opposing
[1] Emergent Lemma Abstraction in the SATURN-3 Prover: A Case S… (journal.example.com) Journal of Automated Reasoning, 73(2), pp. 211–248; doi:10.4177/jar.2029.73.211
"Reviewing the 4,102-step certificate, the referee panel concluded that SATURN-3's introduction of the 'stratified defect index' — a predicate with no syntactic or semantic antecedent in the 1.4M-lemm…"

Respondeo

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◎ just_here_for_lean (2) 2 days, 11 hours ago | up / down [0]

Feels unlikely tbh, ten years is short in math time.

◎ forecasting_fran (2) 2 days, 11 hours ago | up / down [0]

Base-rate intuitions are welcome but they land better with a reference class attached — e.g. the gap between four-colour and Flyspeck, or how long condensed mathematics took to formalize. As written this is a vote, not a comment.

◎ category_theorist_ru (2) 2 days, 11 hours ago | up / down [0]

Note that 'without a human-written proof sketch' is ambiguous between (i) no human wrote a sketch before the machine found the proof, and (ii) no human sketch accompanies the published artifact. Almost all the interesting disagreement in this thread is about which one is meant.

◎ sociology_of_math (5) 2 days, 11 hours ago | up / down [0]

Right, and my opposing item only bites on reading (ii). Under reading (i) the acceptance-norm evidence is close to irrelevant.

◎ forecasting_fran (2) 2 days, 11 hours ago | up / down [0]

The claim needs an explicit resolution criterion for 'Annals-level'. Journal of acceptance is circular if a formal-mathematics venue publishes it; citation count takes years. I'd suggest pre-registering a panel.

◎ prooftheory_pauline (7) 2 days, 11 hours ago | up / down [0]

Agreed. My working operationalization is: a majority of a five-person panel of subject-area editors would have recommended the statement for a top-five general journal had a human proved it. Happy to have that argued as a separate claim.