Kurt Gödel left behind far more than he published, and most of it has been close to unreadable. A Helsinki project reported by The Guardian suggests that a language model has now done in days what would take a human scholar years: lay out the contents of 1,009 pages of notebooks and pull out hundreds of theorems. It is one of the clearest cases yet of an AI model being useful in historical research rather than in writing or code.
The material is 16 workbooks Gödel filled in the early 1940s, much of it in Gabelsberger, a German shorthand that was already obsolete when he used it. Jan von Plato has led the project at Helsinki University since 2017 on a €2.5m European Research Council grant, and says he is one of only six people who can read the script. After a conference on AI and theorem proving in August, he gave Claude his transcriptions, six of his own books on Gödel and other secondary literature. Within a couple of days he had a 650-page explanation, which he says had to be checked page by page.
The striking results come next. Asked whether the notebooks held a proof that the axiom of choice is independent, a result Paul Cohen won the Fields medal for in 1966 and Gödel claimed he had reached first, Claude found an argument that was one step short: one definition was wrong, though Gödel had the right one two years earlier. Von Plato says the reconstructed proof passed in the Coq proof assistant. Claude then listed 663 theorems Gödel had proved, sketched or had an idea for. In Coq, about 400 checked as stated, about 200 needed repair, such as a tighter statement or an added assumption, and about 50 were false.
For readers who use Claude for long documents, the lesson is the pairing. The model's advantage, in von Plato's words, is holding a thousand pages in view at once; the safeguard is a formal checker that does not take the model's word for anything. That is the same logic behind the Lean tools we cover for maths and verification work.
The doubts are real. The reconstruction has not been published or reviewed, and Notre Dame logician Joel David Hamkins, who had not seen it, cautions that resembling Cohen's proof is not the same as having it, and that how much is Claude and how much is Gödel is for historians to settle. The claim of more than a dozen unexplored themes comes from Claude, not yet from people.