03357nam a22005055i 4500 978-3-662-69483-1 DE-He213 20251030112938.0 cr nn 008mamaa 240904s2024 gw | s |||| 0|eng d 9783662694831 978-3-662-69483-1 10.1007/978-3-662-69483-1 doi QA1-939 PB bicssc MAT000000 bisacsh PB thema Müller-Stach, Stefan. author. aut http://id.loc.gov/vocabulary/relators/aut 83735 The Code of Mathematics [electronic resource] : Proof and Truth / by Stefan Müller-Stach. 1st ed. 2024. Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2024. XIII, 170 p. 51 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematics Study Resources, 2731-3832 ; 11 Fundamental Questions -- Scientific Languages -- Mathematical Thinking -- Mathematics in our Culture -- Computability and Decidability -- Deductive Systems and Incompleteness -- Category Theory -- Type Theory -- Semantics and Reality. 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. The Author Stefan Müller-Stach is Vice President for Research and Early Career Academics at Johannes Gutenberg University Mainz and professor for number theory. His main research focus is on algebraic and arithmetic geometry, mathematical physics and history of science. 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. Mathematics. 65523 Mathematics Philosophy. 69649 Mathematics. 65523 Philosophy of Mathematics. 69650 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783662694824 Printed edition: 9783662694848 Mathematics Study Resources, 2731-3832 ; 11 81153 https://doi.org/10.1007/978-3-662-69483-1 ZDB-2-SMA ZDB-2-SXMS 63118 63118