**ABOUT THIS BOOK**In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard's mathematics department was at the center of these developments. *A History in Sum* is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose.

The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics--an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce's successors--William Fogg Osgood and Maxime Bôcher--undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators--students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling.

*A History in Sum* elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.

**REVIEWS**This book tells the tale of how mathematics developed at Harvard--and by extension in the United States--since early days. It is filled with fascinating stories about some of the legendary names of modern mathematics. Both fans of mathematics and readers curious about the history of Harvard will enjoy it.

-- Edward Witten, Professor of Physics, Institute for Advanced Study

*A History in Sum* is a beautiful tribute to a beautiful subject, one that illuminates mathematics through the lens of some of its most remarkable practitioners. The authors' love of mathematics shines through every chapter, as they use accessible and spirited language to describe a wealth of heady insights and the all-too-human stories of the minds that discovered them. There is perhaps no better book for immersion into the curious and compelling history of mathematical thought.

-- Brian Greene, Professor of Mathematics & Physics, Columbia University

The book is written in a leisurely style, the scope is remarkably broad, and the topics covered are explained astonishingly well. Once I started the book, I simply couldn't put it down and I was ecstatic to easily understand important mathematics far from my own research interests.

-- Joel Smoller, Professor of Mathematics, University of Michigan

*A History in Sum* contains a wealth of good stories, stories that go to the heart of the development of mathematics in this country. The authors succeed in humanizing and enlivening what might otherwise be a dry treatment of the subject.

-- Ron Irving, Professor of Mathematics, University of Washington

**Nadis** and **Yau** are very successful at bringing some of the major figures in American mathematics to life. *A History in Sum* is a genuine and valuable addition to the world of mathematical biography.

-- Paul Lockhart, author of *Measurement*

A triumph! I know of no other book like *A History in Sum*. **Nadis** and **Yau** offer a delightfully lucid introduction to the dazzling and heroic ideas of twentieth-century mathematics--and the colorful personalities and stories behind them.

-- Steven Strogatz, author of *The Joy of X: A Guided Tour of Math, from One to Infinity*

The development of American mathematics, and American education more generally, cannot be told without an account of Harvard University…Though a department history seems like a parochial exercise, Harvard’s mathematics department’s history is much bigger and well worth the read.

-- J. McCleary Choice

[An] interesting history of mathematics at Harvard…The book starts from the mid-19th century, when mathematics came into being as an area of study at Harvard University. It reveals a myriad of personalities who have contributed to its prestige as a centre of mathematical research. It portrays life at Harvard from around 1825 to times of the great depression and the years following the 2nd World War. More importantly, it provides meaningful insight into all sorts of mathematical topics.

-- Peter Ruane Mathematical Association of America Reviews

The remarkable result is an account, at a consistently clear, non-specialist level, of a wide swath of modern mathematics.

-- Albert C. Lewis Mathematical Reviews (starred review)

[The authors] treat mathematics of ever-increasing theoretical difficulty with hands that manage deftly…to reveal the spirit, the excitement, and the dynamics of the mathematical endeavor at the cutting edge of research.

-- Karen Hunger Parshall Canadian Journal of History

The story of the Harvard mathematics department’s growth into one of the world’s premier centers of mathematical research is of interest not only in its own right but as a microcosm of the development of the larger American mathematical community. A collaboration between a scientific journalist (**Nadis**) and an eminent Harvard mathematician (**Yau**) has now brought us a very readable account of this history.

-- Gerald B. Folland American Mathematical Monthly

**Yau** and **Nadis** succeed admirably in making clear how Harvard has long served as a magnet, attracting some of the world’s best mathematicians and thus making it an exciting place to be, a melting pot of mathematical activity.

-- Joseph W. Dauben Isis

**TABLE OF CONTENTS**
Contents

Preface

Prologue: The Early Days- A "Colledge" Riseth in the Cowyards

1. Benjamin Peirce and the Science of "Necessary Conclusions"

2. Osgood, Bôcher, and the Great Awakening in American Mathematics

3. The Dynamical Presence of George David Birkhoff

4. Analysis and Algebra Meet Topology: Marston Morse, Hassler Whitney, and Saunders Mac Lane

5. Analysis Most Complex: Lars Ahlfors Gives Function Theory A Geometric Spin

6. The War and Its Aftermath: Andrew Gleason, George Mackey, and an Assignation in Hilbert Space

7. The Europeans: Oscar Zariski, Richard Brauer, and Raoul Bott

Epilogue: Numbers and Beyond

Notes

Index