Graph Theory in America: The First Hundred Years

How a new mathematical field grew and matured in America

Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois.

Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included.

Graph Theory in America tells how a remarkable area of mathematics landed on American soil, took root, and flourished.

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Graph Theory in America: The First Hundred Years

How a new mathematical field grew and matured in America

Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois.

Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included.

Graph Theory in America tells how a remarkable area of mathematics landed on American soil, took root, and flourished.

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Graph Theory in America: The First Hundred Years

Graph Theory in America: The First Hundred Years

Graph Theory in America: The First Hundred Years

Graph Theory in America: The First Hundred Years

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Overview

How a new mathematical field grew and matured in America

Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois.

Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included.

Graph Theory in America tells how a remarkable area of mathematics landed on American soil, took root, and flourished.


Product Details

ISBN-13: 9780691240657
Publisher: Princeton University Press
Publication date: 01/17/2023
Sold by: Barnes & Noble
Format: eBook
Pages: 320
File size: 27 MB
Note: This product may take a few minutes to download.

About the Author

Robin Wilson is emeritus professor of mathematics at the Open University. His many books include Four Colors Suffice (Princeton). John J. Watkins is professor emeritus of mathematics at Colorado College. His books include Topics in Commutative Graph Theory, Number Theory, and Across the Board (all Princeton). David J. Parks received a PhD in mathematics at the Open University. His doctoral thesis forms the basis of this book.

Table of Contents

Foreword vii

Preface ix

Featured Papers xi

Chronology of Events xiii

Setting the Scene: Early American Mathematics 1

Some Early Colleges

Mathematics Education

1 The 1800s 17

James Joseph Sylvester

Alfred Kempe

William Story

C. S. Peirce

Interlude A Graph Theory in Europe 1 52

P. G. Tait (Scotland)

Percy Heawood (England)

Julius Petersen (Denmark)

Lothar Heffter (Germany)

Heinrich Tietze (Austria)

Hermann Minkowski (Germany)

2 The 1900s and 1910s 69

Paul Wernicke

Oswald Veblen

George D. Birkhoff

World War I

3 The 1920s 87

Philip Franklin

H. Roy Brahana

J. Howard Redfield

A Trio of Map Colorers

Interlude B Graph Theory in Europe 2 105

Dénes König (Hungary)

Alfred Errera (Belgium)

André Sainte-Laguë (France)

Karl Menger (Austria)

Kazimierz Kuratowski (Poland)

4 The 1930s 121

Hassler Whitney

Saunders Mac Lane

Academic Life in the 1930s

5 The 1940s and 1950s 154

World War II

Graph Theorists of the 1940s

W. T. Tutte

Algorithms

Frank Harary

6 The 1960s and 1970s 203

Oystein Ore

The Heawood Conjecture

Ron Graham

Complexity

The Four Color Theorem

Aftermath 244

Glossary 253

Notes, References, and Further Reading 263

Acknowledgments and Picture Credits 285

Index 289

What People are Saying About This

From the Publisher

“This fascinating book documents the huge expansion in the range and depth of graph theory, from its first focus on the four color conjecture to the multifaceted subject it is today.”—Peter Cameron, University of St Andrews

“This insightful book tells the story of graph theory’s first century in the United States, taking readers from its arrival from Europe in the late nineteenth century to the unusual solution of the famous four color problem. Graph Theory in America is a remarkable historical journey that sheds light on how advanced mathematics found a place at American universities.”—Ping Zhang, Western Michigan University

“The development of high-level mathematics in North American universities has a long history, and its story provides a fascinating background. Just as seeds mature into thriving plants, early concepts of graph theory in Europe evolved into flourishing fields elsewhere. This book tells the story of that success in America.”—Lowell W. Beineke, coauthor of Line Graphs and Line Digraphs

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