A History in Sum

A History in Sum

Steve Nadis
Shing-Tung Yau
Copyright Date: 2013
Published by: Harvard University Press
https://www.jstor.org/stable/j.ctt6wpqft
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  • Book Info
    A History in Sum
    Book Description:

    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 Sumis an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry, complex analysis, and other esoteric subdisciplines that are rarely 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 transformed the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Influential figures soon flocked to Harvard, some overcoming great challenges to pursue their elected calling.A History in Sumelucidates 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.

    eISBN: 978-0-674-72655-0
    Subjects: Mathematics, Education, History

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. PREFACE
    (pp. ix-xx)
    Shing-Tung Yau and Steve Nadis
  4. PROLOGUE: The Early Days—A “Colledge” Riseth in the Cowyards
    (pp. 1-6)

    The beginnings of Harvard University (originally called “Harvard Colledge” in the vernacular of the day) were certainly humble, betraying little hints of what was in store in the years, and centuries, to come. The school was established in 1636 by decree of the Great and General Court of the Massachusetts Bay Colony, but in that year it was more of an abstraction than an actual institute of higher learning, consisting of neither a building nor an instructor and not a single student. In 1637, or thereabouts, a house and tiny parcel of cow pasture were purchased in “Newetowne” (soon to...

  5. 1 BENJAMIN PEIRCE AND THE SCIENCE OF “NECESSARY CONCLUSIONS”
    (pp. 7-31)

    Benjamin Peirce came to Harvard at the age of sixteen and essentially never left, all the while clinging to the heretical notion that mathematicians ought to dooriginalmathematics, which is to say, they should prove new theorems and solve problems that have never been solved before. That attitude, sadly, was not part of the orthodoxy at Harvard, nor was it embraced at practically any institution of higher learning in the United States. At Harvard and elsewhere, the emphasis was onteachingmath andlearningmath but not ondoingmath. This approach never sat well with Peirce, who was...

  6. 2 OSGOOD, BÔCHER, AND THE GREAT AWAKENING IN AMERICAN MATHEMATICS
    (pp. 32-55)

    As the first person to conduct significant mathematical research at the school, Benjamin Peirce was truly a Harvard pioneer, even if he was practically the only one doing such work, and even if he had to fit in those efforts between the chores that actually paid his bills: teaching and writing textbooks. The next leap forward for the Harvard mathematics department was made around the turn of the twentieth century by William Fogg Osgood and Maxime Bôcher, who turned Harvard into a power house in the field of analysis—a branch of pure mathematics that includes calculus, as well as...

  7. 3 THE DYNAMICAL PRESENCE OF GEORGE DAVID BIRKHOFF
    (pp. 56-85)

    Within a year of joining the Harvard faculty in 1912, George David Birkhoff had knocked off a celebrated problem, posed by Henri Poincaré, that would earn him international fame. Birkhoff solved a version of the three-body problem, which involves describing motions in a system of three gravitating objects such as the sun, Earth, and the moon. The eminent mathematician Poincaré had framed the classic problem in a new way. And since his health was failing at the time, he had put the problem out to the rest of the world, hoping that someone might find a way through it. That...

  8. 4 ANALYSIS AND ALGEBRA MEET TOPOLOGY: MARSTON MORSE, HASSLER WHITNEY, AND SAUNDERS MAC LANE
    (pp. 86-115)

    In contemplating the legacy of George David Birkhoff, who has been called (justifiably so) a “towering figure” in American mathematics,¹ we ought to consider more than his intellectual achievements or the personal shortcomings described in Chapter 3. We should also take into account his leadership role in the field, as well as the remarkable group of graduate students he trained at Harvard. In the preface of this book, we used the metaphor of a river to describe the flow of ideas in mathematics. But one can also invoke the notion of a family tree, starting with luminaries like Leonhard Euler...

  9. 5 ANALYSIS MOST COMPLEX: LARS AHLFORS GIVES FUNCTION THEORY A GEOMETRIC SPIN
    (pp. 116-140)

    Born in 1907 in Helsinki, Finland, Lars Ahlfors was the first European mathematician to hold a permanent position on the Harvard mathematics faculty. In deviating from its traditional policy of recruiting “home-grown” American mathematicians, the department was hardly taking a chance in 1946 when it hired Ahlfors (following a three-year visiting appointment from 1935 to 1938), since by that time he had already established himself as an international star of the first rank. In 1936, Ahlfors was the winner (along with Jesse Douglas of MIT) of the first Fields Medal ever offered—a prize that has since come to be...

  10. [Illustrations]
    (pp. None)
  11. 6 THE WAR AND ITS AFTERMATH: ANDREW GLEASON, GEORGE MACKEY, AND AN ASSIGNATION IN HILBERT SPACE
    (pp. 141-165)

    The bombing of Pearl Harbor brought World War II home to the United States in a dramatic, as well as deadly, fashion. Following the attack on December 7, 1941, which left 2,400 Americans dead and thirty U.S. ships damaged or destroyed, the country immediately went to war, issuing a formal declaration the next day. More than ten million American men and women enlisted in the military during this struggle—a massive involvement that extended deeply into academia. Harvard was no exception. Its math department thinned out significantly during World War II, with mathematicians joining the armed forces or volunteering as...

  12. 7 THE EUROPEANS: OSCAR ZARISKI, RICHARD BRAUER, AND RAOUL BOTT
    (pp. 166-203)

    In the late 1930s and early 1940s, before and during World War II, a wave of European mathematicians, most of whom were Jewish, migrated to the United States. Although the total number of mathematicians was not especially large—an estimated 120 to 150 émigrés had arrived by the end of the war—many of these individuals were scholars of the first rank, and their influence was widely felt on the American mathematical scene.¹

    As discussed in Chapter 3, Harvard’s math department was mostly untouched by the influx of European refugees until after the war. Lars Ahlfors, who was Finnish but...

  13. EPILOGUE: Numbers and Beyond
    (pp. 204-210)

    While trying to lure Raoul Bott to Harvard in 1959, John Torrence Tate was facing a quandary of his own. Although he had been employed at Harvard since 1954, Princeton had just made him an offer—sparked by some exciting work Tate had just completed while on sabbatical in Paris—that was too tempting to ignore. Bott’s decision to come to Cambridge helped persuade Tate to stay put; the presence of the talented, as well as charismatic, Bott in the department instantly made Harvard a more attractive place to be. Tate’s decision, in turn, had profound consequences for Harvard, as...

  14. NOTES
    (pp. 211-240)
  15. INDEX
    (pp. 241-250)