The Proof and Truth Müller-Stach, Stefan. creator author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text gw 2024 1st ed. 2024. monographic eng

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access XIII, 170 p. 51 illus. online resource. 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. Fundamental Questions -- Scientific Languages -- Mathematical Thinking -- Mathematics in our Culture -- Computability and Decidability -- Deductive Systems and Incompleteness -- Category Theory -- Type Theory -- Semantics and Reality. by Stefan Müller-Stach. Mathematics Mathematics Philosophy Mathematics Philosophy of Mathematics QA1-939 9783662694831 https://doi.org/10.1007/978-3-662-69483-1 https://doi.org/10.1007/978-3-662-69483-1 240904 20251030112938.0 978-3-662-69483-1