An investigation of 16 notebooks by Kurt Gödel, with 1,009 pages, identified 663 possible theorems with the help of Claude, Anthropic's artificial intelligence model. The work was conducted by mathematician Jan von Plato, of the University of Helsinki, and its results were reported by the British newspaper The Guardian on Friday the 13th.
The manuscripts, written in the 1940s, contain research on mathematics and logic, much of it recorded in Gabelsberger, an old German shorthand system. Since 2017, von Plato's team had been investigating the material but was progressing at approximately one page per week.
In September 2026, the researcher began using Claude to analyze the transcriptions of the notebooks, along with related books and studies. In a few days, the AI produced a synthesis of approximately 650 pages, making it possible to connect information scattered throughout the manuscripts.
“The AI can connect all the parts of a thousand pages,” von Plato told The Guardian. The researcher stressed, however, that the material produced required page-by-page review.
Results identified by the AI required corrections and verification
After the initial analysis, von Plato asked Claude to identify all the theorems for which Gödel had recorded complete proofs, sketches or ideas for proofs. The system presented 663 results, later examined with Coq, a formal verification tool for mathematical proofs.
According to the researcher, about 400 were verified as presented, approximately 200 required adjustments to their statements or the hypotheses used, and about 50 were considered false.
Among the findings is an attempted proof of the independence of the axiom of choice, a mathematical question associated with the work that earned Paul Cohen the Fields Medal in 1966. The reconstruction examined by von Plato passed verification in Coq but contained a definition that Gödel had formulated incorrectly.
Mathematician Joel David Hamkins, of the University of Notre Dame, warned that the similarity to Cohen's proof does not prove that Gödel reached the same result decades earlier.
The investigation also pointed to 14 topics in logic not yet explored, according to the assessment reported by von Plato. The researcher intends to continue examining the manuscripts, including notebooks dedicated to physics and cosmology.
