On November 13, 2026, The Guardian reported that an AI model helped unlock hundreds of previously unknown results in the notebooks of Kurt Gödel. Alex Bellos writes that Helsinki logician Jan von Plato used Anthropic's Claude on 1,009 pages of Gödel's workbooks. Claude returned a digest in days, and a proof assistant then checked what it found.
The story is a clean example of AI used for science with a built-in check. It is also a story with open claims. This post separates what is reported, what was machine-verified, and what historians still have to decide.
TL;DR: what is claimed and what is verified
| Item | Status |
|---|---|
| 16 notebooks, 1,009 pages, written in the early 1940s | Described in the Guardian report and the Helsinki project |
| Text is in Gabelsberger, an obsolete German shorthand | Reported |
| Human pace was about a page a week | Von Plato's account |
| Claude produced a 650-page explanation in "a couple of days" | Von Plato's account, checked page for page by him |
| 663 theorems extracted | Reported |
| About 400 verified as stated in Coq, about 200 repaired, about 50 false | Von Plato's figures, reported by The Guardian |
| Gödel was "one step away" from the independence of the axiom of choice | Von Plato's claim, passed Coq in reconstructed form; not yet reviewed by outside logicians |
Who is Jan von Plato and what are the workbooks?
Gödel's two incompleteness theorems, published in 1931, changed mathematics and fed into the ideas behind computing. After the 1930s he published little, but left tens of thousands of pages of unpublished work. Since 2017, von Plato has led a project at the University of Helsinki on 16 notebooks Gödel wrote in the early 1940s, the "workbooks."
The project, described by the University of Helsinki, is funded by an ERC grant. The Guardian gives the figure as 2.5 million euros. The text is hard in two ways. It is dense mathematics and logic, and much of it is written in Gabelsberger shorthand. Von Plato taught himself to read it. He says he is one of only six people who can.
Progress was slow: about a page a week. That is the baseline the AI result should be compared with.
What happened in September
In August, von Plato attended a conference in France on AI and theorem proving. Computer scientists there suggested he try Claude. Back in Helsinki in September, he showed the model his transcriptions of the workbooks, his six earlier books on Gödel and other secondary literature.
Within a couple of days he saw a 650-page explanation of the material. He told The Guardian it had to be controlled page for page. He also said it is "basically a work that is impossible to do for human beings," because people read one page at a time and forget parts. His argument is about scale: the model can hold the connections across a thousand pages at once.
This is long-context reading used as a research assistant, not a new proof engine. The same pattern appears in other recent AI-for-math work, such as Claude's machine-checked proof of Fermat's Last Theorem in Lean and OpenAI's Lean collaborations. What is different here is the source: a human historian's transcription, checked against a proof assistant.
The axiom of choice question
The first task von Plato gave Claude was historical. In 1966 Paul Cohen won the Fields medal for showing that the continuum hypothesis and the axiom of choice are independent of standard set theory. Gödel reacted by saying he had proved the result in the 1940s. When peers pushed for the proof, he could not reconstruct it from his notes.
Von Plato asked whether the workbooks held a proof of the independence of the axiom of choice. The answer, as he reports it, was "yes, almost." One definition was wrong, but Gödel had the right definition two years earlier. Von Plato thinks Gödel would have reached the correct one within months. He ran the reconstructed proof through Coq, a proof assistant that checks the validity of proofs, and it passed.
Von Plato believes that, had Gödel published it, he would have won the 1940 Fields medal. That is an opinion, not a verified fact.
The 663 theorems and the 400 / 200 / 50 split
Von Plato then asked Claude to extract every theorem in the workbooks where Gödel had a proof, a sketch or an idea. Claude found 663. After the formal check, von Plato says:
- About 400 were verified as stated.
- About 200 were repaired. The statement needed to be made more precise or an assumption added.
- About 50 were false.
The false ones are not a surprise. Von Plato notes that Gödel himself sometimes wrote "falsch!" or "schlecht!" in the margins when rereading. He also says the notebooks contain dozens of anticipations of results not known until the 1970s and 1980s, and 14 themes in logic that have not been pursued.
The split is the useful part for anyone using AI on research. A model will give you a confident list. A checker sorts it into pass, fix and fail. Without Coq, the 50 false items would sit in the list looking the same as the 400 true ones.
What experts say
The Guardian quotes Joel David Hamkins, a logic professor at the University of Notre Dame. He has not seen Claude's reconstruction. He says that if it stands up, it is "remarkable and historically interesting." He adds that how much comes from Claude and how much from Gödel is a job for historians.
He also draws a line on credit. Resemblance to Cohen's proof, he says, shows Gödel was on the path, not that he had it. "You don't get credit for work you don't tell anyone about," in his words. That caution is the right frame for the headline: "hundreds of proved theorems" describes what the notebooks are said to contain, and the open question is which parts are Gödel's ideas and which are Claude's repair work.
What is not known yet
- No paper or data release has been reported, so outside logicians cannot rerun the extraction.
- The 650-page digest has been checked by von Plato, but not by independent reviewers that we know of.
- The Coq results cover the formal statements. They do not settle whether Gödel held the proof in his head.
- The Guardian report does not name the Claude model version or give the cost.
- Further notebooks, including physics and cosmology, are planned. Von Plato says he will start those after his current logic projects.
Why the historical stakes are real
Gödel's incompleteness theorems showed that in any consistent mathematical system of enough strength, some true statements can be neither proved nor disproved inside it. That result ended a hope held by earlier logicians that every truth could be verified. It also pushed Alan Turing to write his 1936 paper that began the theory of modern computation.
Gödel then fled Austria in 1940, settled in Princeton and became a close friend of Albert Einstein at the Institute for Advanced Study. The workbooks come from this period. They sit between his famous 1930s results and the set-theory work on the continuum hypothesis and the axiom of choice. If the reconstruction holds, historians gain a clearer picture of how far Gödel got in those years and why he felt overlooked when Cohen's medal arrived in 1966.
It also shows a limit of the method. A model can read a thousand pages and link ideas across them, but it cannot say what Gödel privately believed. Von Plato admires how Gödel "starts from ideas" and then proceeds methodically, step after step. That reading of intent is a human judgment, and the proof assistant only confirms that the final statements are valid.
What builders can take from this
- Pair the generator with a checker. The strongest part of this story is the Coq step. The model proposes, the proof assistant disposes. The same shape works for code and tests.
- Give the model your own context. Von Plato supplied his transcriptions and six books, not just the scans. Domain material changed the output from a summary into a research digest.
- Review at the page level. He controlled the digest "page for page." Plan for a human pass on long outputs.
- Report three buckets. Verified, repaired and false is more honest than one accuracy figure. It echoes the point in Anthropic's own guide to strong safety evals: report the breakdown, not just the headline.
For more on claims made with formal proofs, see our claimed-versus-verified check on a finite simple groups result, Lean retrieval tooling and free formal verification for open source.
Related reading
- Claude wrote a machine-checked proof of Fermat's Last Theorem
- OpenAI: three results with Lean collaborations
- Finite simple groups classification in Lean: claimed vs verified
- LeanGraphSearch for Lean 4 theorem proving
- Theorem OSS Verify: free formal verification
- Anthropic's guide to building strong safety evaluations
- Sources: The Guardian report, University of Helsinki Gödel project
Details are accurate as of November 13, 2026. Figures are von Plato's, as reported by The Guardian.