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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Allg. & Lexika Can Mathematics Be Proved Consistent?
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Can Mathematics Be Proved Consistent?
Jan von Plato (Broschiert, 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 composed.The 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.07.2021
Sprache
Englisch
EAN
9783030508784
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Sources and Studies in the History of Mathematics and Physical Sciences
Sonderedition
Nein
Autor
Jan von Plato
Seitenanzahl
263
Einbandart
Broschiert
Buch Untertitel
Gödel's Shorthand Notes & Lectures on Incompleteness
Schlagwörter
incompleteness theorems, Skolem's paradox, Principia Mathematica, completeness problem, German mathematicians, Gödel lectures, Gödel incompleteness theorem, Gödel notes, Open Access
Thema-Inhalt
PBX - Geschichte der Mathematik
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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