Researchers working on Austrian logician Kurt Gödel’s unpublished notebooks have made significant breakthroughs with the assistance of artificial intelligence. Jan von Plato, a Finnish logician leading a project at Helsinki University since 2017, has been studying 16 notebooks Gödel wrote in the early 1940s. The workbooks comprise over 1,000 pages of densely written mathematical and logical content, much of it in Gabelsberger shorthand, an obsolete German stenographic system. Progress through manual analysis had been extremely slow, averaging approximately one page per week.
In September, von Plato enlisted the AI model Claude to assist with the analysis. Within days, Claude produced a comprehensive summary of the entire material, dramatically accelerating the research. The analysis revealed that Gödel had proved hundreds of theorems previously unknown to the academic community. Von Plato noted that the workbooks contain dozens of mathematical results that would not be independently discovered until the 1970s and 1980s, as well as 14 unexplored logical themes.
Among the significant findings is evidence supporting Gödel’s 1966 claim that he had already proved the independence of the axiom of choice in the 1940s. Mathematician Paul Cohen had received the Fields Medal in 1966 for demonstrating this independence, but Gödel said he had achieved the same result decades earlier. Von Plato’s team used the AI-reconstructed proof and verified it through the Coq proof verification system. The analysis identified 663 theorems in the workbooks for which Gödel possessed either complete proofs, proof sketches, or developed ideas.
Von Plato began the Gödel project in 2017 with support from a €2.5 million European Research Council grant, teaching himself Gabelsberger shorthand to access the material. He states he is one of only six people worldwide capable of reading the script. The collaboration with Claude demonstrates how artificial intelligence can facilitate historical research by synthesizing vast amounts of complex information that would be impractical for human researchers to process comprehensively.
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