Kurt Gödel, widely regarded as one of the most innovative thinkers of the 20th century, left behind an immense archive of unpublished research that has long puzzled historians. Renowned for his 1931 incompleteness theorems, which fundamentally transformed mathematics and provided a foundation for the digital era, Gödel published very little after his initial breakthroughs. However, his private legacy includes tens of thousands of pages of notes, including 1,009 pages of dense mathematical and logical writing known as his “workbooks,” penned during the early 1940s in a rarely used German shorthand called Gabelsberger. Oh yes, I’ll start reading Gödel’s enigmatic shorthand pages. He has very, very clear ideas, and then he’s methodical.
Since 2017, Jan von Plato, a logician at the University of Helsinki, has spearheaded an effort to transcribe and interpret these 16 notebooks. The project faced significant logistical hurdles, as the obscure shorthand required specialized knowledge and the sheer complexity of the material was daunting for manual analysis. Progress was initially slow, with researchers managing only about a page per week until von Plato integrated the AI model Claude into the research process this past September. According to von Plato, He had started his Gödel project in 2017 because he was facing mandatory retirement from Helsinki University. “What should I do to make myself indispensable. “What strikes me especially is that he starts from ideas.
By feeding his transcriptions and existing secondary literature into the AI, von Plato achieved a breakthrough in understanding the documents. Within days, Claude provided a comprehensive digest of the material, suggesting that the Austrian logician had formulated hundreds of theorems that were previously unknown to the academic community. Von Plato, who noted that he was “flabbergasted” by the findings, stated that the workbooks contain not only anticipations of research that did not emerge until the 1970s and 1980s but also over a dozen distinct logical themes that have remained unexplored for more than 80 years. According to “I was flabbergasted,”, Von Plato. “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. “In a couple of days, I got to see a 650-page explanation of the workbooks. His physics and cosmology notebooks are an unknown territory I plan to start exploring once I am finished with my present logic projects.”.
Gödel’s career was marked by his profound influence on the limits of mathematical knowledge.
His famous theorems demonstrated that all mathematical systems contain truths that cannot be proven or disproven within that system.
This discovery, while challenging, propelled new fields of study and influenced pioneers like Alan Turing. After fleeing Nazi-occupied Austria in 1940, Gödel moved to Princeton, New Jersey, where he became a close companion of Albert Einstein at the Institute of Advanced Study. In his final years, he suffered from declining mental health, dying of starvation in 1978 due to extreme paranoia surrounding his food. Who had hoped that all truths were verifiable, Gödel’s work pushed the field in new directions, inspiring Alan Turing to write his 1936 paper that began the theory of modern computation, yet while this result was a blow to previous generations of logicians. In 1940, Gödel fled Austria under the Nazis. He refused to eat food that was not cooked by his wife, and died of starvation in 1978, increasingly paranoid in his later years. We just are not able to keep in mind all the different parts. He’s not like someone who plays with formulas and hopes to arrive somewhere. Step after step he goes ahead and he manages to fulfil the aims that he has in this formal work.”.
Von Plato, who secured a €2.5 million grant from the European Research Council for this work, taught himself the archaic Gabelsberger shorthand to begin the project. He described the AI’s contribution as transformative, noting that while human researchers struggle to synthesize thousands of pages of complex data, the model could view Gödel’s body of work as a unified whole. “Humans read one page at a time and we tend to forget things… The AI can connect all the pieces in a thousand pages,” he explained.
A specific goal of the project was to investigate a long-standing claim regarding the independence of the axiom of choice. In 1966, mathematician Paul Cohen was awarded a Fields medal for proving the independence of the continuum hypothesis and the axiom of choice. Gödel had asserted at the time that he had reached the same conclusion in the 1940s but could not reconstruct the proof from his notes. When von Plato tasked Claude with analyzing the workbooks, the AI revealed that Gödel had indeed been essentially correct, requiring only one adjustment to a definition that he had, in fact, utilized correctly two years earlier. In August, at a conference in France about AI and theorem proving, von Plato met computer scientists who suggested that he co-opt the help of Claude in trying to make sense of the workbooks. Which would reveal that Gödel had been telling the truth in 1966, the first task von Plato set Claude was to discover if Gödel’s workbooks had a proof of the independence of the axiom of choice. According to the answer came back: yes, almost. “He was just one step away,”, Von Plato. “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 definition anyway if he had just continued for a few months. According to joel David Hamkins, a professor of logic at the University of Notre Dame, Indiana, has not seen Claude’s reconstruction of Gödel’s proof of the independence of the axiom of choice, but, If it stood up “it is remarkable and historically interesting.
The AI’s reconstruction of this proof was subsequently verified using Coq, a program designed to confirm the validity of mathematical reasoning. Von Plato believes that had Gödel published these results at the time, he would likely have been the recipient of the 1940 Fields medal.
Beyond this specific proof, the team used the AI to catalog 663 theorems found within the notebooks. Using the Coq verification tool, researchers confirmed 400 were accurate as written, while 200 required minor corrections or additional assumptions to be precise. Approximately 50 were identified as false, a finding that correlates with Gödel’s own handwritten marginal notes where he occasionally labeled his work as “falsch” (incorrect) or “schlecht” (bad). Moving forward, von Plato intends to continue mining these manuscripts, confident that the AI-assisted analysis will uncover further hidden scientific treasures. About 200 were repaired, meaning that perhaps the statement of the theorem had to be made more precise, or some assumption had to be added, when these results were put into Coq: “About 400 were verified as stated.
