Can Mathematics Be Proved Consistent?

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Sprache: Englisch

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Beschreibung

Kurt Gödel (1906¿1978) shook the mathematical world in 1931 by a result that has become an icon of 20th century science: The search for rigour in proving mathematical theorems had led to the formalization of mathematical proofs, to the extent that such proving could be reduced to the application of a few mechanical rules. Gödel showed that whenever the part of mathematics under formalization contains elementary arithmetic, there will be arithmetical statements that should be formally provable but aren¿t. The result is known as Gödel¿s first incompleteness theorem, so called because there is a second incompleteness result, embodied in his answer to the question "Can mathematics be proved consistent?"

This book offers the first examination of Gödel¿s preserved notebooks from 1930, written in a long-forgotten German shorthand, that show his way to the results: his first ideas, how they evolved, and how the jewel-like final presentation in his famous publication On formally undecidable propositions was [...] book also contains the original version of Gödel¿s incompleteness article, as handed in for publication with no mentioning of the second incompleteness theorem, as well as six contemporary lectures and seminars Gödel gave between 1931 and 1934 in Austria, Germany, and the United States. The lectures are masterpieces of accessible presentations of deep scientific results, readable even for those without special mathematical training, and published here for the first time.

Zusammenfassung

Contains a thorough introduction to a very important mathematician's research

Features a series of lectures and seminars based on Gödel's results

Includes a translation of Gödel's manuscripts from German Gabelsberger shorthand to English

Inhaltsverzeichnis

I. Gödel's Steps Toward Incompleteness.- II. The Saved Sources on Incompleteness.- III. The Shorthand Notebooks.- IV. The Typewritten Manuscripts.- V. Lectures and Seminars on Incompleteness.- Index.- References.

Details

Erscheinungsjahr:	2021
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Inhalt:	ix 263 S.
ISBN-13:	9783030508784
ISBN-10:	3030508781
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Plato, Jan Von
Auflage:	1st edition 2020
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 16 mm
Von/Mit:	Jan Von Plato
Erscheinungsdatum:	26.07.2021
Gewicht:	0,423 kg