Great Feuds in Mathematics

Hal Hellman

Description

Praise for Hal Hellman

Great Feuds in Mathematics

"Those who think that mathematicians are cold, mechanical proving machines will do well to read Hellman's book on conflicts in mathematics. The main characters are as excitable and touchy as the next man. But Hellman's stories also show how scientific fights bring out sharper formulations and better arguments."
-Professor Dirk van Dalen, Philosophy Department, Utrecht University

Great Feuds in Technology

"There's nothing like a good feud to grab your attention. And when it comes to describing the battle, Hal Hellman is a master."
-New Scientist

Great Feuds in Science

"Unusual insight into the development of science . . . I was excited by this book and enthusiastically recommend it to general as well as scientific audiences."
-American Scientist

"Hellman has assembled a series of entertaining tales . . . many fine examples of heady invective without parallel in our time."
-Nature

Great Feuds in Medicine

"This engaging book documents [the] reactions in ten of the most heated controversies and rivalries in medical history. . . . The disputes detailed are . . . fascinating. . . . It is delicious stuff here."
-The New York Times

"Stimulating."
-Journal of the American Medical Association
Acknowledgments.

Introduction.

1. Tartaglia versus Cardano • Solving Cubic Equations.

2. Descartes versus Fermat • Analytic Geometry and Optics.

3. Newton versus Leibniz • Credit for the Calculus.

4. Bernoulli versus Bernoulli • Sibling Rivalry of the Highest Order.

5. Sylvester versus Huxley • Mathematics: Ivory Tower or Real World?

6. Kronecker versus Cantor • Mathematical Humbug.

7. Borel versus Zermelo • The “Notorious Axiom”.

8. Poincaré versus Russell • The Logical Foundations of Mathematics.

9. Hilbert versus Brouwer • Formalism versus Intuitionism.

10. Absolutists/Platonists versus Fallibilists/Constructivists • Are Mathematical Advances Discoveries or Inventions?

Epilogue.

Notes.

Bibliography.

Index.

Sujets

• Sciences et techniques
• Mathematics

Informations

• Publié par: Turner Publishing Company
• Date de parution: 17 décembre 2010
• Nombre de lectures: 0
• EAN13: 9781118040119
• Langue: English

Extrait

Table of Contents
 
Title Page
Copyright Page
Acknowledgments
Introduction
 
Chapter 1 - Tartaglia versus Cardano
 
Rebirth
Tartaglia
Cardano, Renaissance Man
Preliminaries
A Sacred Promise?
A Battle Not-So-Royal
A First Attempt
A Shadowy Hand
Who Won?
 
Chapter 2 - Descartes versus Fermat
 
Descartes
Certainty and Method
Descartes’ “Geometry”
Dismay—and Conflict
Fermat, the Hesitant Amateur
Attack and Response
Anger Builds
Things May Not Be What They Seem
Continuing Provocation
Retaliation
Comparison
 
Chapter 3 - Newton versus Leibniz
 
Newton
Publish or . . .
Leibniz
Notation
Other Players
Flashpoint
Further Conflict
A Question Mark
Was There Plagiarism?
Unexpected Outcome
Who Deserves the Credit?
 
Chapter 4 - Bernoulli versus Bernoulli
 
Some Background
The Kid Brother
Their Young Years
The Relationship Changes
Calculus of Variations
Battle Lines
Even in Death
Johann Carries On
Still More Controversy
And Yet Again
 
Chapter 5 - Sylvester versus Huxley
 
Huxley before Sylvester’s Challenge
Darwin’s Bulldog
And in the Other Corner
Sylvester’s Response
Huxley after Sylvester
Sylvester after Huxley
 
Chapter 6 - Kronecker versus Cantor
 
Kronecker
Cantor and His Strange Ideas
Infinite Set Theory
Set Theory Is Born
Conflict Begins
Cantor’s Later Years
The Point of Madness
Invitations to the Dance
A New Century
Summation
 
Chapter 7 - Borel versus Zermelo
 
Zermelo
Borel
Axiomatics
More Work
Incompleteness
 
Chapter 8 - Poincaré versus Russell
 
Russell
Logicism
Logicism Emerges, Warts and All
Poincaré
Response
Counterattack
And So It Goes
Russell, after Poincaré
 
Chapter 9 - Hilbert versus Brouwer
 
Beginnings of Formalism
The Mouse
The Frog
Counterattack(s)
A Ruthless Attack
The Frog and Mouse War
The Winner and New Champion
 
Chapter 10 - Absolutists/Platonists versus Fallibilists/Constructivists
 
A Collection of Diamonds to Be Discovered
Mathematical Knowledge Is Created
Mathematics Is Both Invention and Discovery
Is There a Crisis in Education?
Pedagogy and Philosophy
 
Epilogue
Notes
Bibliography
Index

Copyright © 2006 by Hal Hellman. All rights reserved
 
Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada
 
Design and composition by Navta Associates, Inc.
 
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Library of Congress Cataloging-in-Publication Data:
 
Hellman, Hal, date.
Great feuds in mathematics : ten of the liveliest disputes ever / Hal Hellman. p. cm.
Includes bibliographical references and index.
ISBN-13 978-0-471-64877-2 (cloth) ISBN-10 0-471-64877-9 (cloth)
1. Mathematics—History. 2. Mathematicians—History. I. Title.
QA21.H45 2006
510—dc22
2005031916

 
Acknowledgments
A book like this required that I sort through an enormous amount of material. The Internet was convenient, quick, slow, amazing, and frustrating, not necessarily in that order. It brought me material I could never have gotten otherwise. For the depth and the continuity I needed, however, printed books and journals were still my primary sources. The collections at the New York Public Library and the newer Science, Industry, and Business Library, both in Manhattan, provided much useful information.
Mostly, I would like to thank the staff at my own library in Leonia, New Jersey. My local branch is, happily, part of a countywide system, which widens the collection considerably. Special thanks go to Gina Webb-Metz and Teresa Wyman, reference librarians, who managed to draw in a remarkable selection of materials from across the country.
Many colleagues have helped as well. Some were kind enough to read and comment on sections of the manuscript in progress. Among them: William Dunham, Professor of Mathematics at Muhlenberg College, Allentown, Pennsylvania; Daniel Curtin, Professor of Mathematics at Northern Kentucky University, Highland Heights, Kentucky; Professor Joseph W. Dauben, Ph.D. Program in History, City University of New York, New York City; Siegmund Probst, Professor of Mathematics, University of Hannover, Germany; and Dirk van Dalen, Professor of Philosophy, Utrecht University, the Netherlands.
Some of the material was available only in the original French, which I, unfortunately, cannot handle. I also needed help with some German translations and even a few pages in Spanish. Help in these areas came from Daniel Curtin, mentioned previously; J. D. Nicholson, independent scholar, Baltimore, Maryland; Eric J. Simon, Professor of Psychiatry and Pharmacology at New York University Medical Center, New York City; Fred Stern, independent scholar and lecturer, Leonia, New Jersey; and Laura Mausner, translator, Teaneck, New Jersey.
Yet others helped in some way: by sending me useful material, answering specific questions, or talking through ideas with me. These include Susana Mataix, independent scholar, Madrid, Spain; Stephen Gaukroger, Professor of the History of Philosophy and the History of Science at the University of Sydney, Sydney, Australia; Michael Sean Mahoney, Professor of History at Princeton University, Princeton, New Jersey; Rüdiger Thiele, Professor of Medicine, University of Leipzig, Germany; Richard Bronson, Professor of Mathematics at Fairleigh Dickinson University, Teaneck, New Jersey; Richard Lyons, Professor of Mathematics at Rutgers University, Piscataway, New Jersey; Marshall Hurwitz, Professor Emeritus of Classics, City University of New York, and Arthur Peck, friend, polymath, and retired psychiatrist, Tenafly, New Jersey.
Additional thanks go to my editor, Stephen Power, who believed in the project and provided needed encouragement along the way; to my agent, Faith Hamlin, for her continued and helpful support; and to Fay Klein, who was always there when I needed her.
Introduction
When my editor at John Wiley & Sons suggested that I do a book on great feuds in mathematics, I was not excited by the idea. I had taken some mathematics in school for my master’s degree in physics, but that was long ago and I had not used any of it for a very long time. Furthermore, I knew nothing of mathematics’ history. Most of all, though, my idea of mathematics was just plain old-fashioned. Mathematics, I felt, is a cold, logical discipline where questions can be decided, if not quickly, at least objectively and decisively. As opposed to, say, politics or religion, or even science, there is little room for human emotions and sensitivities. How could there be feuds in mathematics?
Still, I consulted with an acquaintance, a professor of mathematics, and asked him about the idea. He shook his head and, without giving it a second thought, said, “You’ll be lucky if you come up with two feuds.”
This fitted in with ideas I could recall from earlier readings. Bertrand Russell, for example, had written, “Mathematics, rightly viewed, possesses not only truth but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.” 1
Isn’t it strange how we continue to find what we want to find? As I searched further, I came up with a similar idea from another of my favorite authors, Morris Kline: “Keen minds seeking to establish new systems of thought on the basis of certain cogent knowledge were attracted by the certitude of mathematics, for the truths of mathematics . . . had really never been challenged or been subject to the slightest doubt by the true scholars. Moreover, mathematical demonstrations carried with them a compulsion and an assurance that had not been equaled in science, philosophy, or religion.” 2
I came very close to giving a definite no to my editor, but he, happily, persevered, and so did