The Proof is in the Pudding

The Changing Nature of Mathematical Proof

Authors: Krantz, Steven G

  • An extensive evolution of the proof presented for the first time in book form
  • Covers centuries of mathematical history, dating back to Eudoxus and Euclid and concluding with versatile, present-day use of the proof
  • Expresses keen insights and a wealth of historical knowledge
  • Proofs presented are accompanied by figures, equations and examples
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  • ISBN 978-0-387-48744-1
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Hardcover $49.99
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  • ISBN 978-0-387-48908-7
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About this book

Krantz’s book covers the full history and evolution of the proof concept.   The notion of rigorous thinking has evolved over time, and this book documents that development.   It gives examples both of decisive developments in the technique of proof and also of magnificent blunders that taught us about how to think rigorously.  Many historical vignettes illustrate the concepts and acquaint the reader with how mathematicians think and what they care about.

In modern times, strict rules for generating and recording proof have been established.  At the same time, many new vectors and forces have had an influence over the way mathematics is practiced.  Certainly the computer plays a fundamental role in many mathematical investigations.

But there are also fascinating social forces that have affected the way that we now conceive of proof.   Daniel Gorenstein’s program to classify the finite simple groups, Thomas Hales’s  resolution of the Kepler sphere-packing problem, Louis de Branges’s proof of the Bieberbach conjecture, and Thurston’s treatment of the geometrization program are but some examples of mathematical proofs that were generated in ways inconceivable 100 years ago.  Krantz treats all of them---and more---in some detail; he names the players and tells all the secrets.

Many of the proofs treated in this book are described in some detail, with figures and explanatory equations. The reader is given a dose of modern mathematics, and h

ow mathemati

cians think.   Both the joy and the sorrow of mathematical exploration are communicated dynamically and energetically in this exciting new book.

About the authors

Steven Krantz is a well-known Springer author. He has written nine books with Springer (1-931914-59-1, 0-8176-4339-7, 0-8176-4011-8, 0-8176-4339-7, 0-8176-4220-X, 0-8176-4097-5, 1-930190-87-5, 0-8176-4264-1, 0-8176-4285-4 ) with sales accumulating almost $130,000 in North America. Prof. Krantz is the editor-in-chief of the "society" journal (published in cooperation with Springer) "The Journal of Geometric Analysis" and is also the present editor-in-chief of the AMS Notices. "The Proof is in the Pudding, is the first of its kind. It details the history of the proof from its beginnings to its place in present-day mathematics. (This was presented as a "hot topic" in an article in the Notices of the AMS.)

Reviews

“This book is to describe the essence, nature, and methodology of mathematical proof, with a strong emphasis on the change of these concepts in time. … It is written in a very clear and suggestive manner that makes the reading pleasant and rewarding … . Any reader will notice that the author has reached this goal in very convincing way, and the outcome is a brilliant work which should be found in every math library and department office.” (Jürgen Appell, zbMATH 1318.00005, 2015)

“In this book Steven Krantz undertakes the Miltonic task of justifying the ways of (pure) mathematicians to the world at large. … The concept of mathematical proof is at the heart of Krantz’s book. … mathematicians should find the book interesting, illuminating, provocative … .” (J. M. Plotkin, Mathematical Reviews, Issue 2012 b)

“The author traces the development of the idea of proof from Euclid through computer-aided and computer-generated proofs, pointing out the way some current social trends in mathematics affect the construction of nonstandard proofs. … This work provides good outside class reading for students--and not just mathematics majors; one could easily imagine this as a supplement to courses on the history or philosophy of science. Summing Up: Recommended. Lower-division

undergraduates through researchers/faculty; general readers.” (D. Robbins, Choice, Vol. 49 (2), October, 2011)

“Krantz’s book is entertaining, can be read by the early undergraduate and puts forward some serious issues. There are few math books that are useful and valuable reading for all mathematicians, but this is one of them.” (Charles Ashbacher, The Mathematical Association of America, June, 2011)




Table of contents (13 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-0-387-48744-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.99
price for USA
  • ISBN 978-0-387-48908-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Proof is in the Pudding
Book Subtitle
The Changing Nature of Mathematical Proof
Authors
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-387-48744-1
DOI
10.1007/978-0-387-48744-1
Hardcover ISBN
978-0-387-48908-7
Edition Number
1
Number of Pages
XVII, 264
Number of Illustrations and Tables
83 b/w illustrations, 5 illustrations in colour
Topics