ENGLISH

The Code of Mathematics

By Stefan Müller-Stach

Book information

Publisher
Springer
Year
2024
ISBN
9783662694824, 9783662694831
Language
english
Format
PDF
Filesize
5 MB (4912014 bytes)
Pages
177\177
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2024-09-06 19:38:18

Description

Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. Besides selected ideas of Platon, Aristoteles, Leibniz, Kant, Frege and others, the results of Gödel and Tarski on incompleteness, undecidability and truth in deductive systems and their semantic models are covered. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory. Such theories contain identity types, which give a new understanding of equality, symmetry, equivalence and isomorphism in a conceptual way. The interaction of type theory and infinity category theory yields a new paradigm for a structural view on mathematics. This supports the tendencies towards formalising mathematics with the help of proof assistants. This book was first published in German. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.

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