Sources and Studies in the History of Mathematics and Physical Sciences

Can Mathematics Be Proved Consistent?

Gödel's Shorthand Notes & Lectures on Incompleteness

Authors: von Plato, Jan

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  • 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
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  • ISBN 978-3-030-50876-0
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valid through June 30, 2021
  • ISBN 978-3-030-50875-3
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About this book

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.

Table of contents (5 chapters)

Table of contents (5 chapters)
  • Gödel’s steps toward incompleteness

    Pages 1-28

    von Plato, Jan

  • The saved sources on incompleteness

    Pages 29-58

    von Plato, Jan

  • The shorthand notebooks

    Pages 59-168

    von Plato, Jan

  • The typewritten manuscripts

    Pages 169-200

    von Plato, Jan

  • Lectures and seminars on incompleteness

    Pages 201-260

    von Plato, Jan

Buy this book

eBook $19.99
$44.99 (listprice)
price for USA
valid through June 30, 2021
  • ISBN 978-3-030-50876-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $29.99
$59.99 (listprice)
price for USA
valid through June 30, 2021
  • ISBN 978-3-030-50875-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock

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Bibliographic Information

Bibliographic Information
Book Title
Can Mathematics Be Proved Consistent?
Book Subtitle
Gödel's Shorthand Notes & Lectures on Incompleteness
Authors
Series Title
Sources and Studies in the History of Mathematics and Physical Sciences
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-50876-0
DOI
10.1007/978-3-030-50876-0
Hardcover ISBN
978-3-030-50875-3
Series ISSN
2196-8810
Edition Number
1
Number of Pages
IX, 263
Topics