03005nam a22004215i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001500165072002300180072001400203100008500217245009900302250001800401264008200419300004500501336002600546337002600572338003600598347002400634490005000658505023900708520131400947650001702261650002902278650001702307650003102324710003402355773002602389776003602415776003602451830005002487856004602537978-3-662-69483-1DE-He21320251030112938.0cr nn 008mamaa240904s2024 gw | s |||| 0|eng d a97836626948317 a10.1007/978-3-662-69483-12doi 4aQA1-939 7aPB2bicssc 7aMAT0000002bisacsh 7aPB2thema1 aMüller-Stach, Stefan.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut14aThe Code of Mathematicsh[electronic resource] :bProof and Truth /cby Stefan Müller-Stach. a1st ed. 2024. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg :bImprint: Springer,c2024. aXIII, 170 p. 51 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aMathematics Study Resources,x2731-3832 ;v110 aFundamental Questions -- Scientific Languages -- Mathematical Thinking -- Mathematics in our Culture -- Computability and Decidability -- Deductive Systems and Incompleteness -- Category Theory -- Type Theory -- Semantics and Reality. aInspired 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. 0aMathematics. 0aMathematicsxPhilosophy.14aMathematics.24aPhilosophy of Mathematics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978366269482408iPrinted edition:z9783662694848 0aMathematics Study Resources,x2731-3832 ;v1140uhttps://doi.org/10.1007/978-3-662-69483-1