Project description
Studying the minds behind modern mathematics
Three pioneers of modern logic and the foundations of mathematics, Kurt Gödel, Gerhard Gentzen, and Paul Bernays, transformed the field, yet much of their work remains hidden in cryptic shorthand. Their notebooks and lecture notes explore the consistency of analysis, intuitionistic methods, computable functionals, and the structure of formal proofs, ideas that underpin mathematical philosophy and modern computation. The ERC-funded HERITAGE project aims to make these sources accessible. Specifically, it will transcribe and translate them into English for the first time. A team of experts will then study the material, exploring how these abstract concepts were taught and understood. The findings are expected to open a new window on 20th-century mathematics.
Objective
"The project's aims are the transcription from shorthand and study of the writings of Kurt Gödel, Gerhard Gentzen, and Paul Bernays on the main problem of the foundations of mathematics, namely the consistency of analysis. These rich sources have remained inaccessible because of their archaic shorthand. Previous work by the PI on Gödel's and Gentzen's shorthand notes has led to stunning discoveries published in many articles and eight books, but it has left the said main problem untouched. The most important uncharted source in Gödel are his 16 ""Arbeitshefte,"" each running up to a hundred pages, and developing topics such as intuitionistic analysis and computable functionals. With Gentzen, the main sources, in another shorthand, are his two long series of notes, the ""WA"" (Consistency of analysis) and the ""BTIZ"" (Proof theory of intuitionistic arithmetic). With Bernays, the main sources are his detailed notes for two lecture courses on logic in Göttingen, in 1927 and 1929-30 that surpass by a wide margin anything known before about the birth of today's logic. The first phase of transcription and translation into English of the project aims at finishing volumes that contain all these source materials.
After the first phase, a second, interpretive phase of study will be carried through. This is done in collaboration with six leading experts, chosen from different domains so that their expertise as a whole encompasses the topics and results uncovered by the first phase of the project.
The project as a whole points at a new approach to the historical study of the development of science and philosophy: It is estimated that there exist thousands of exact recordings of lecture courses in shorthand by students, what are called ""Mitschriften."" The study of these vast sources will open up a new, third type of sources in the history of science, next to (a) publications and author manuscripts and (b) correspondence: How were the new theories presented to students?
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Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- humanities history and archaeology history
- natural sciences mathematics pure mathematics arithmetics
- humanities philosophy, ethics and religion philosophy
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
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(opens in new window) ERC-2024-ADG
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00014 HELSINGIN YLIOPISTO
Finland
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