Evidence against: 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 ◎ kernel_purist_9 (13) · 2 months ago

The vote is on the link: is “Kernel-level trust in Lean is illusory because every large formalization to dat…” good evidence against the claim?

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.
sources
[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…”
the evidence

Kernel-level trust in Lean is illusory because every large formalization to date has relied on axioms or porting steps outside the verified core

An audit of the eight largest Mathlib-dependent developments found each invokes at least one of: classical choice with unchecked instance resolution, native_decide compilation, or a trusted C++ extension. Therefore a machine-generated proof would not in fact be verified, and the claim cannot be satisfied under any circumstances.

◎ kernel_purist_9 (13) · 2 months ago · formal-verification · logic
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 ◎ mathlib_maintainer_ines (5) · 2 months ago

Choice is in the axiom list by design; calling that 'outside the verified core' is a category error. native_decide is a real concern and there's a linter that flags it — usage is under 0.2% of declarations.

0 ◎ kernel_purist_9 (13) · 2 months ago

0.2% of declarations can still be load-bearing for the theorem you care about.

0 ◎ brunner_fm (15) · 2 months ago

True in principle, and that's why the axiom-dependency command exists — you can check per-theorem. That makes it an auditing task, not an in-principle barrier, which is what the parent claims.

0 ◎ grad_student_lurker (2) · 2 months ago

Downvoting rather than replying at length: the leap from 'some developments use native_decide' to 'the claim cannot be satisfied under any circumstances' is not an argument.