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 B cher--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.
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About the Author
Shing-Tung Yau, a Fields Medal winner, is William Caspar Graustein Professor of Mathematics and former chair of the Mathematics Department at Harvard University.
Table of Contents
Prologue: The Early Days-A "Colledge" Riseth in the Cowyards 1
1 Benjamin Peirce and the Science of "Necessary Conclusions" 7
2 Osgood, Bôcher, and the Great Awakening in American Mathematics 32
3 The Dynamical Presence of George David Birkhoff 56
4 Analysis and Algebra Meet Topology: Marston Morse, Hassler Whitney, and Saunders Mac Lane 86
5 Analysis Most Complex: Lars Ahlfors Gives Function Theory a Geometric Spin 116
6 The War and Its Aftermath: Andrew Gleason, George Mackey, and an Assignation in Hilbert Space 141
7 The Europeans: Oscar Zariski, Richard Brauer, and Raoul Bott 166
Epilogue: Numbers and Beyond 204