The Proof is in the Pudding
The Changing Nature of Mathematical Proof
Authors: Krantz, Steven G
Free Preview 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, presentday 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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 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 spherepacking 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 themand morein 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 mathematicians 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 wellknown Springer author. He has written nine books with Springer (1931914591, 0817643397, 0817640118, 0817643397, 081764220X, 0817640975, 1930190875, 0817642641, 0817642854 ) with sales accumulating almost $130,000 in North America. Prof. Krantz is the editorinchief of the "society" journal (published in cooperation with Springer) "The Journal of Geometric Analysis" and is also the present editorinchief 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 presentday 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 computeraided and computergenerated 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 studentsand not just mathematics majors; one could easily imagine this as a supplement to courses on the history or philosophy of science. Summing Up: Recommended. Lowerdivision
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)


What Is a Proof and Why?
Pages 136

The Ancients
Pages 3746

The Middle Ages and An Emphasis on Calculation
Pages 4752

The Dawn of the Modern Age
Pages 5359

Hilbert and the Twentieth Century
Pages 61106

Table of contents (13 chapters)
 Download Preface 1 PDF (116.4 KB)
 Download Sample pages 1 PDF (684.1 KB)
 Download Table of contents PDF (113.3 KB)
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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

 Steven G Krantz
 Copyright
 2011
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media, LLC
 eBook ISBN
 9780387487441
 DOI
 10.1007/9780387487441
 Hardcover ISBN
 9780387489087
 Softcover ISBN
 9781493938834
 Edition Number
 1
 Number of Pages
 XVII, 264
 Number of Illustrations
 83 b/w illustrations, 5 illustrations in colour
 Topics