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The code of mathematics = proof and ...

Müller-Stach, Stefan.

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The code of mathematics = proof and truth /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The code of mathematics/ by Stefan Müller-Stach.
Reminder of title:	proof and truth /
Author:	Müller-Stach, Stefan.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2024.,
Description:	xiii, 170 p. :ill., digital ;24 cm.
[NT 15003449]:	Fundamental Questions -- Scientific Languages -- Mathematical Thinking -- Mathematics in our Culture -- Computability and Decidability -- Deductive Systems and Incompleteness -- Category Theory -- Type Theory -- Semantics and Reality.
Contained By:	Springer Nature eBook
Subject:	Mathematics - Philosophy. -
Online resource:	https://doi.org/10.1007/978-3-662-69483-1
ISBN:	9783662694831

The code of mathematics = proof and truth /
Müller-Stach, Stefan.

The code of mathematicsproof and truth /[electronic resource] :by Stefan Müller-Stach. - Berlin, Heidelberg :Springer Berlin Heidelberg :2024. - xiii, 170 p. :ill., digital ;24 cm. - Mathematics study resources,v. 112731-3832 ;. - Mathematics study resources ;v. 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.

ISBN: 9783662694831

Standard No.: 10.1007/978-3-662-69483-1doiSubjects--Topical Terms:

523930
Mathematics
--Philosophy.

LC Class. No.: QA8.4

Dewey Class. No.: 510.1

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520 $a 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.
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