In pursuit of Gentzen's consistency programme.

• Applicant: Daniel Misselbeck-Wessel, Ph.D.
• Subject Area: History of Science
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 554603079

The foundational crisis of mathematics stands as one of the defining scientific challenges of the early 20th century. In its aim to establish a demonstrably consistent foundation, the Hilbert program introduced the metamathematical perspective. However, this endeavor proved infeasible in its original ambition in light of Gödel’s incompleteness theorems. Gerhard Gentzen (Greifswald 1909 - Prague 1945) succeeded in solving the situation created by Gödel’s insights. The development of his formal proof systems and Gentzen’s consistency proofs for number theory still witness his brilliance and far-reaching influence today. It was by chance that a collection of Gentzen’s notes was discovered in the 1980s. However, it took several more decades before this scientific legacy could reveal its full value. The deciphering of these writings has once again stalled, primarily due to a particular inherent difficulty: the manuscripts were written in shorthand. This project aims to undertake an extensive study of Gentzen’s notes from the period 1938-45. These writings encompass Gentzen’s approach to the consistency problem of analysis, as well as previously unknown draft chapters of Gentzen’s habilitation thesis. These manuscripts are to be translated, interpreted, and thus made accessible to a broader, international audience.

• DFG Programme: Research Grants