Jan von Plato, a logician at the University of Helsinki, has used the AI model Claude to decode 1,009 pages of handwritten notes by Kurt Gödel. The work, published in late 2026, reveals that the Austrian mathematician proved hundreds of theorems that remained unknown for decades. The discovery confirms that Gödel was significantly ahead of his time in mathematical logic.
Decoding Gabelsberger Shorthand
Gödel wrote the notebooks in the early 1940s using Gabelsberger shorthand, an obsolete German system that even experts find difficult to read. Von Plato, who is one of only six people in the world who can read the script, began studying the material in 2017. Progress was slow, with the team deciphering roughly one page per week.
The breakthrough came in September when von Plato introduced Claude to the transcribed text. The AI model processed the entire 1,009-page collection in a few days. It generated a 650-page digest that connected ideas across the notebooks, a task von Plato said would take humans a year to complete.
“The AI can connect all the pieces in a thousand pages. It can see all of Gödel’s writings as one piece,” von Plato said. “Humans read one page at a time and we tend to forget things.”
Verification of Mathematical Proofs
The AI analysis identified 663 theorems in the notebooks where Gödel had a proof, a sketch, or an idea. Von Plato ran these results through Coq, a program that verifies mathematical proofs. About 400 theorems were verified as stated. Approximately 200 required minor repairs to their statements or assumptions. About 50 were found to be false, a result consistent with Gödel’s own marginal notes where he marked certain ideas as incorrect.
A key finding involved the independence of the axiom of choice. Gödel had claimed in 1966 that he had already proven this result, but he could not reconstruct the proof from his notes. Claude’s analysis showed that Gödel was indeed one step away from a complete proof. The AI reconstructed an architecture that von Plato verified using Coq. The proof follows a uniform pattern that von Plato described as wonderful.
Von Plato believes that if Gödel had published this work on the axiom of choice, he might have won the 1940 Fields medal. Gödel died in 1978, and the full extent of his unpublished work remains a subject of intense study.
Historical Impact and Future Research
The discovery adds to the understanding of Gödel’s influence on modern mathematics. His incompleteness theorems, published in 1931, transformed the field by showing the limits of mathematical knowledge. This work inspired Alan Turing to write his 1936 paper on computation.
Joel David Hamkins, a professor of logic at the University of Notre Dame, noted that the findings are historically interesting. He said that while Gödel was on the path to these results, the credit for the work belongs to those who published it. “You don’t get credit for work you don’t tell anyone about,” Hamkins said.
Von Plato plans to continue exploring the notebooks. He said the work contains more than a dozen themes in logic that have not been pursued in the 80 years since they were written. He also intends to study Gödel’s physics and cosmology notebooks next.
Source: The Guardian
