AI unlocks Gödel's notebooks, said to contain hundreds of proved theorems

Kurt Gödel, one of the most original thinkers of the 20th century, left behind 1,009 pages of densely written text in notebooks, some containing hundreds of proved theorems. After his groundbreaking work on incompleteness theorems in 1931, Gödel published only a few papers, leaving behind a massive amount of unpublished work. In 2017, Finnish logician Jan von Plato led a project at Helsinki University to decipher 16 notebooks written by Gödel in the early 1940s.

Initially, the progress was slow, as the material contained 1,009 pages of densely written text in an obsolete German shorthand. However, in September, with the help of AI model Claude, von Plato made substantial progress, revealing that Gödel had proved hundreds of theorems unknown to others. Von Plato was astonished by the discovery, as the workbooks contained anticipations of results not known until the 1970s and 80s, as well as 14 themes in logic that had not been pursued.

Gödel's incompleteness theorems demonstrated the limitations of mathematical knowledge, leaving previous generations of logicians in the dust. These theorems showed that in all mathematical systems, there are true statements that cannot be proved or disproved, thus paving the way for new directions in the field. Gödel fled Austria under the Nazis and settled in Princeton, becoming a close friend of Albert Einstein.

In 1940, he died of starvation after refusing food not cooked by his wife. Von Plato started his Gödel project in 2017 due to his mandatory retirement and received a €2.5m grant from the European Research Council. The AI model Claude played a crucial role in understanding the workbooks, providing a comprehensive digest of the material and revealing Gödel's far-ahead-of-his-time discoveries.