AI unlocks Gödel's notebooks, revealing hundreds of proved theorems

Finnish logician Jan von Plato used Claude to digest 1,009 pages of Kurt Gödel's 1940s Gabelsberger-shorthand workbooks, a task that had been progressing at about a page a week. Claude produced a 650-page explanation and identified 663 theorems Gödel had proved, sketched or conceived; when run through the Coq proof assistant, about 400 verified as stated, about 200 needed repair and about 50 were false. Von Plato said Claude's reconstruction of a proof of the independence of the axiom of choice, which passed Coq, suggests Gödel had the result in the 1940s, and that the workbooks contain more than a dozen unexplored themes in logic.