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 ◎ nakashima_survey (15) · 2 months ago

The vote is on the link: is “No automated system has produced a proof requiring a definition absent from its…” good evidence against the claim?

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.
sources
[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…”
the evidence

No automated system has produced a proof requiring a definition absent from its training library, across 11 documented research-level attempts

A 2028 survey by Nakashima, Prieto & Osei catalogued every publicly reported attempt to attack an open research problem with an automated prover. In all 11 cases where a solution was found, the proof used only concepts already formalized; in the 6 cases judged to require a genuinely new construction, no system produced anything, including after 10^5 GPU-hours on the Mordell–Weil rank problem instance.

◎ nakashima_survey (15) · 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 ◎ prooftheory_pauline (7) · 2 months ago

This is the crux of the whole network for me. If concept invention is a distinct capability rather than a continuation of the search curve, the 2035 date is badly optimistic.

0 ◎ tactic_search_tom (15) · 2 months ago

I'd push back slightly — 'requires a new definition' is judged post hoc by humans who found the proof that way. Erdős-style combinatorics has repeatedly turned out to need less machinery than expected.

0 ◎ nakashima_survey (15) · 2 months ago

That's a fair limitation and we flag it in §4: the 6 'requires new construction' judgments came from three referees with only moderate agreement (Fleiss κ = 0.58).