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_2thema
100 1 _aMüller-Stach, Stefan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_983735
245 1 4 _aThe Code of Mathematics
_h[electronic resource] :
_bProof and Truth /
_cby Stefan Müller-Stach.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aXIII, 170 p. 51 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
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490 1 _aMathematics Study Resources,
_x2731-3832 ;
_v11
505 0 _aFundamental Questions -- Scientific Languages -- Mathematical Thinking -- Mathematics in our Culture -- Computability and Decidability -- Deductive Systems and Incompleteness -- Category Theory -- Type Theory -- Semantics and Reality.
520 _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.
650 0 _aMathematics.
_965523
650 0 _aMathematics
_xPhilosophy.
_969649
650 1 4 _aMathematics.
_965523
650 2 4 _aPhilosophy of Mathematics.
_969650
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662694824
776 0 8 _iPrinted edition:
_z9783662694848
830 0 _aMathematics Study Resources,
_x2731-3832 ;
_v11
_981153
856 4 0 _uhttps://doi.org/10.1007/978-3-662-69483-1
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