The Code of Mathematics

Name: The Code of Mathematics
Price: 101.37 AUD
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ISBN: 9783662694824

Proof and Truth

Stefan Müller-Stach

$126.95 $101.37

Paperback

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German

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
04 September 2024

Philosophy of mathematics

Series: Mathematics Study Resources

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.

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.

By: Stefan Müller-Stach
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: 2024 ed.
Volume: 11
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783662694824
ISBN 10: 3662694824
Series: Mathematics Study Resources
Pages: 170
Publication Date: 04 September 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Fundamental Questions.- Scientific Languages.- Mathematical Thinking.- Mathematics in our Culture.- Computability and Decidability.- Deductive Systems and Incompleteness.- Category Theory.- Type Theory.- Semantics and Reality.

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.

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The Code of Mathematics

Proof and Truth

Stefan Müller-Stach

$126.95 $101.37

Paperback

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