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Markdown edition

# AI helps researchers examine Gödel notebooks

> Human transcripts help researchers explore unfinished arguments.

By BIGCHANGE.AI Editorial

Published: 2026-11-13T20:47:38.842Z
Updated: 2026-11-13T20:47:38.842Z
Canonical: https://bigchange.ai/blog/godel-notebooks-ai-reconstruction

![Illustration of a researcher comparing a transcript and laptop.](https://bigchange.ai/api/media/file/archive-v2.png)
AI-generated illustration for BIG CHANGE.

On November 13, von Plato told [The Guardian](https://www.theguardian.com/science/2026/nov/13/kurt-godel-notebooks-ai-helps-unlock-hidden-discoveries-man-who-transformed-maths) his reconstructed independence proof for the axiom of choice passed Coq.

Logician Jan von Plato's AI-assisted study of Kurt Gödel's notebooks was already described in October. Its starting point was human transcription, followed by Claude's analysis of the resulting English text.

## The big change

- Human transcription makes the notebooks accessible to a language model. In the reported workflow, Claude analyzes English text supplied by a researcher; it does not independently decipher the original shorthand.
- The axiom of choice concerns selecting elements from collections of sets. Its independence means that the usual remaining set-theory axioms cannot settle it, assuming those axioms are consistent.
- Formal verification and historical interpretation answer different questions. A proof assistant checks a precisely stated argument under explicit assumptions; establishing what an earlier author actually discovered also requires examining the historical record.

## From shorthand to reconstruction

The Stanford Encyclopedia's [archival overview](https://plato.stanford.edu/archives/spr2026/entries/goedel/documents.html) describes Gödel's surviving material in German, English and Gabelsberger shorthand, including completed and partially completed manuscripts. That variety matters: a private draft can preserve an idea without presenting a finished argument. Transcription aims to render the marks as text; interpretation asks what the argument means.

[Der Standard](https://www.derstandard.at/story/3000000344396/raetsel-um-verlorenen-goedel-beweis-geloest) reported on October 19 that von Plato supplied hundreds of pages of English transcriptions to Claude on September 24. It described an AI reconstruction from an unfinished approach in the notebooks and continuing correctness checks with computer scientist Josef Urban. Those are attributed research claims, not a reproduction performed for this article.

## What independence means

The Stanford Encyclopedia's [choice entry](https://plato.stanford.edu/entries/axiom-choice/) defines the principle through a choice function: a rule assigning one member to each nonempty set in a collection. For example, from every pair of real numbers, choosing the smaller number provides such a function. The general principle extends beyond collections with an obvious selection rule.

Gödel established relative consistency of choice with Zermelo–Fraenkel set theory; Cohen established its independence in 1963. Assuming that background theory is consistent, adding either choice or its negation remains consistent. The question is therefore not whether AI has first settled this mathematical problem. It is whether a reconstruction illuminates an earlier, unfinished route to an already established result.

## Checking an argument and its history

[Rocq](https://rocq-prover.org/), formerly Coq, is an interactive proof assistant for formal specifications and mathematical proofs. A formalization must specify its statement, definitions and assumptions. Checking that formalization addresses whether the conclusion follows within that system; it cannot establish who first had an idea or whether a transcription faithfully captures an author's intentions.

Readers assessing a reconstructed argument should therefore distinguish the manuscript, its transcription, the proposed mathematical steps and the formalized statement. An added assumption can change what has been proved. A sound proof and a sound attribution both matter, but evidence for one does not automatically establish the other.

## Sources

- [The Guardian](https://www.theguardian.com/science/2026/nov/13/kurt-godel-notebooks-ai-helps-unlock-hidden-discoveries-man-who-transformed-maths) — November interview.
- [Der Standard](https://www.derstandard.at/story/3000000344396/raetsel-um-verlorenen-goedel-beweis-geloest) — October interview.
- [Gödel documents](https://plato.stanford.edu/archives/spr2026/entries/goedel/documents.html) — Archive context.
- [Axiom of choice](https://plato.stanford.edu/entries/axiom-choice/) — Historical mathematical context.
- [Rocq Prover](https://rocq-prover.org/) — Proof assistant background.