Claude AI Uncovers Hundreds of Math Results in Mathematician’s Notebooks

Researchers at the University of Helsinki have used Anthropic’s Claude AI to uncover hundreds of previously overlooked mathematical results in notebooks written more than 80 years ago by influential mathematician Kurt Gödel.

The discovery comes from a research project led by Finnish logician Jan von Plato, who has spent nearly a decade studying 16 notebooks containing 1,009 pages of mathematical work, much of it written in an obsolete German shorthand system.

According to The Guardian, the team had been interpreting the material at roughly one page per week before introducing Claude in September 2026. Within days, the AI produced a 650-page analysis of the notebooks, identifying mathematical arguments and connections that had previously escaped researchers.

Gödel is best known for his incompleteness theorems, published in 1931, which fundamentally changed mathematical logic and influenced the development of modern computing.

The AI-assisted analysis identified 663 mathematical statements that Gödel had proved, outlined, or considered. Researchers subsequently examined the findings using Coq, a software system designed to verify mathematical proofs.

Approximately 400 results were verified as stated, another 200 required corrections or additional assumptions, and around 50 were found to be false.

One significant finding suggests Gödel came close to proving the independence of the axiom of choice decades before mathematician Paul Cohen established the result. Researchers identified an incorrect definition in Gödel’s argument, although he had used the correct definition elsewhere in his notes.

A reconstructed version of the proof passed Coq verification, but that does not establish that Gödel himself completed the original proof.

The research builds on the University of Helsinki’s Gödel Enigma project, which aims to recover and interpret thousands of pages of previously unpublished mathematical writings.

Researchers emphasized that Claude worked with human-prepared transcriptions and supporting literature rather than independently deciphering the original handwriting. Its findings also required mathematical verification and historical interpretation.

The team believes further examination could reveal additional insights into Gödel’s unpublished work, including notebooks covering physics and cosmology.