Claude decodes Gödel notebooks, unearths 600 theorems

Pairing frontier LLMs with formal proof assistants turns historical mathematical archaeology into an automated pipeline, moving AI reasoning far beyond casual code generation.

• –Long-context synthesis solved a ten-year bottleneck: human researchers deciphered Gödel's obsolete Gabelsberger shorthand at just one page per week, while Claude digested 1,009 pages in days to link disconnected mathematical concepts across volumes.
• –The neurosymbolic loop worked: Claude extracted 663 theorem candidates that were fed directly into Coq, where 400 were verified as stated, 200 required minor repairs, and 50 were confirmed false matching Gödel's own marginal doubts.
• –Historical re-evaluation confirmed: Claude reconstructed a near-complete proof of the independence of the axiom of choice, showing Gödel was a single definition away from preempting Paul Cohen's 1963 Fields Medal result.
• –A template for legacy system excavation: combining large-context language models with deterministic formal verifiers demonstrates a reliable blueprint for analyzing legacy codebases, lost technical specs, and complex mathematical archives without hallucination risks.