國立高雄大學圖資館 |

Language: English

Back

The code of mathematicsproof and truth /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The code of mathematicsby 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.
Contained By:	Springer Nature eBook
Subject:	MathematicsPhilosophy.
Online resource:	https://doi.org/10.1007/978-3-662-69483-1
ISBN:	9783662694831$q(electronic bk.)

The code of mathematicsproof 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 ;Band 2..

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$q(electronic bk.)

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

187658
Mathematics
--Philosophy.

LC Class. No.: QA8.4

Dewey Class. No.: 510.1

The code of mathematicsproof and truth /
LDR:02671nmm a22003615a 4500 001 668178
003 DE-He213
005 20240904130728.0
006 m d
007 cr nn 008maaau
008 250107s2024 gw s 0 eng d
020 $a 9783662694831$q(electronic bk.)
020 $a 9783662694824$q(paper)
024 7 $a 10.1007/978-3-662-69483-1 $2 doi
035 $a 978-3-662-69483-1
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA8.4
072 7 $a PB $2 bicssc
072 7 $a MAT000000 $2 bisacsh
072 7 $a PB $2 thema
082 0 4 $a 510.1 $2 23
090 $a QA8.4 $b .M958 2024
100 1 $a Müller-Stach, Stefan. $3 981103
240 1 0 $a Code der Mathematik. $l English
245 1 4 $a The code of mathematics $h [electronic resource] : $b proof and truth / $c by Stefan Müller-Stach.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2024.
300 $a xiii, 170 p. : $b ill., digital ; $c 24 cm.
347 $a text file $b PDF $2 rda
490 1 $a Mathematics study resources, $x 2731-3832 ; $v v. 11
505 0 $a Fundamental Questions -- Scientific Languages -- Mathematical Thinking -- Mathematics in our Culture -- Computability and Decidability -- Deductive Systems and Incompleteness -- Category Theory -- Type Theory -- Semantics and Reality.
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.
650 0 $a Mathematics $x Philosophy. $3 187658
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Philosophy of Mathematics. $3 745264
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Mathematics study resources ; $v Band 2. $3 939447
856 4 0 $u https://doi.org/10.1007/978-3-662-69483-1
950 $a Mathematics and Statistics (SpringerNature-11649)