LLM Lean Proofs for Navier-Stokes Blow-Up and Quasi-Riemann Hit 100k+ Lines with No Readable Translation

Maggi documents the shift from informal proof generation to formal Lean output. Recent LLM systems have closed specific open problems under forcing terms or weakened hypotheses, but the resulting artifacts require separate verification teams. Lean 4 formalization length now correlates inversely with translation fidelity, a pattern observed across multiple theorem-proving benchmarks since 2023.

Data from proof-assistant repositories show median verified statement length rising from 2,000 lines in 2022 to over 80,000 lines for frontier claims in 2025. Human comprehension studies on miniF2F and ProofNet subsets report assimilation rates below 15 percent once length exceeds 10,000 lines. No public dataset yet tracks downstream citation or extension of these machine proofs by independent researchers.

Operational consequence is bifurcation of mathematical labor. One cohort maintains formal libraries and LLM pipelines; the other must treat outputs as black-box oracles. Without new intermediate representations, the second cohort loses the ability to modify or generalize results. Existing open-collaboration norms erode when only centralized compute clusters can iterate on the formal codebase.

Next threshold is deployment of automated explanation layers that reduce effective proof length to human-scale. Absent measurable progress on that metric by 2027, the fraction of new results that remain assimilable by unaided mathematicians will continue to decline.