Artificial Intelligence1 min read

‘Ahead of his time’: AI helps unlock discoveries hidden in notebooks of man who transformed maths

By · Via The Guardian · Published by Everything Blog

In short

Led by Jan von Plato at Helsinki University, a research team spent years transcribing 16 of Gödel's notebooks written in an obsolete shorthand called Gabelsberger. The AI model Claude subsequently processed these transcriptions to produce a 650-page analytical report within just a few days. The findings revealed that Gödel mapped out 14 completely unpursued themes in logic and missed proving the independence of the axiom of choice by only a single step.

Key points

  • Modern artificial intelligence can rapidly analyze complex historical archives that took…: Modern artificial intelligence can rapidly analyze complex historical archives that took human scholars years to transcribe manually.
  • The newly analyzed notebooks prove that Gödel discovered far more modern mathematics than…: The newly analyzed notebooks prove that Gödel discovered far more modern mathematics than was previously recognized by historians.
  • Gödel came within a single step of proving the independence of the axiom of choice decade…: Gödel came within a single step of proving the independence of the axiom of choice decades before Paul Cohen's breakthrough.

Sources checked by our analysis pipeline: 1

The Austrian logician Kurt Gödel was one of the most original thinkers of the 20th century. His two incompleteness theorems, published in 1931, transformed mathematics and paved the way for the digital age.

After his seminal results of the 1930s, Gödel published only a few papers. His unpublished work, however, runs to tens of thousands of pages, and is of great interest to historians of science.

Since 2017, the Finnish logician Jan von Plato has led a project at Helsinki University to understand the contents of 16 notebooks that Gödel wrote in the early 1940s. This material – the “workbooks” – is 1,009 pages of densely written text about maths and logic. Much of it is written in a German shorthand, Gabelsberger, that was obsolete even when Gödel was using it.

Progress in the mathematical understanding of the text was painfully slow – about a page a week – until September, when von Plato enlisted the help of the AI model Claude. Within a couple of days, Claude had provided a comprehensive digest of the entire material, revealing Gödel had…

Artificial Intelligence