Kurt Gödel, the logician who transformed 20th-century mathematics, left behind thousands of pages of unpublished work written in an obsolete shorthand that almost no one alive can read. Now artificial intelligence has helped decode them — and the results suggest the century's most famous mathematical mind was even more prolific than historians believed.
According to a report published Friday by The Guardian, an AI-assisted analysis of Gödel's notebooks has revealed that he proved hundreds of theorems that no one knew about, including results that anticipated developments in mathematical logic from the 1970s and 1980s. For more context on this story, see our ongoing latest AI developments.
A Cryptic Archive Only Six People Can Read
The story begins with the Finnish logician Jan von Plato of Helsinki University, who has led a project since 2017 to understand the contents of 16 notebooks Gödel wrote in the early 1940s, known as the workbooks. The material runs to 1,009 pages of densely written text about mathematics and logic, much of it composed in Gabelsberger, a German shorthand that was already going out of use when Gödel wrote in it.
Von Plato told The Guardian he is one of only six people in the world who can read the shorthand. Progress on the mathematical understanding of the text was painfully slow — about one page a week — despite funding from a €2.5 million (£2.1 million) grant from the European Research Council.
Claude Digests 1,009 Pages in Days
That pace changed in September, when von Plato enlisted the help of Claude, the AI model developed by Anthropic. The idea came in August, at a conference in France about AI and theorem proving, where computer scientists suggested he co-opt the model's help in making sense of the workbooks.
On his return to Helsinki, von Plato began showing Claude his transcriptions of the workbooks, along with six books he had previously written on Gödel and other secondary scientific literature. Within a couple of days, the model had produced a comprehensive digest of the entire material — a 650-page explanation of the workbooks.
"I was flabbergasted," von Plato told The Guardian. "The workbooks not only contain dozens of anticipations of results not known until the 70s and 80s, but they also contain 14 themes in logic that have not been pursued. Gödel was far ahead of his time."
He was careful to note the AI output required verification: "It had to be controlled page for page, but it's basically a work that is impossible to do for human beings," he said. "Humans read one page at a time and we tend to forget things. It takes us a year to read about 50 pages. We just are not able to keep in mind all the different parts."
"The AI can connect all the pieces in a thousand pages," he added. "It can see all of Gödel's writings as one piece."
Testing Gödel's 1966 Claim
One of the first tasks von Plato set Claude carried particular historical weight. In 1966, the American mathematician Paul Cohen won the Fields Medal for proving the independence of two famous mathematical statements: the continuum hypothesis and the axiom of choice. Gödel reacted to Cohen's prize by claiming he had already proved the axiom-of-choice result in the 1940s — yet when pressed by his peers, he was unable to reconstruct a proof from his notes.
Von Plato asked Claude to determine whether the workbooks actually contained a proof of the independence of the axiom of choice. The answer came back: yes, almost. "He was just one step away," von Plato told The Guardian. "There's one definition that Gödel got wrong, but he had the right definition two years earlier, and so the thought is that he would have arrived at the right one."
In other words, Gödel's decades-old claim appears to have been substantially true — his notes got him within a single defective definition of a result that won the field's highest honor.
Why the Gödel Result Matters for AI
The project is a compelling demonstration of AI as a scholarly instrument rather than a replacement for scholarship. The digest was checked page by page by one of the few humans capable of reading the source material, and its value came from holding an entire archive in view at once — a task that exceeds any human reader's working memory, but not a language model's context window.
It also lands at a moment of intense debate about AI's role in mathematics. As our earlier coverage of Terence Tao's essay on AI and mathematics noted, leading mathematicians are openly discussing how machine assistance will reshape discovery and proof. The Gödel workbooks offer a concrete early example: not AI proving new theorems, but AI revealing how much human genius had already proven and never published.
For the history of logic, the findings suggest that dozens of results credited to later decades had precursors sitting unread in Princeton archives, and that 14 unexplored themes in Gödel's notes may still seed new work. For AI research, the episode is a case study in verification-first collaboration: the model produced a synthesis no human could, and the human caught, checked and contextualized every page of it.
Gödel, who fled Austria in 1940 and became Albert Einstein's close friend at Princeton's Institute for Advanced Study, died in 1978. Four decades later, the notebooks he left behind are finally being read in full — with help from a machine, guided by one of the six people on Earth who could have done it alone.
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