A History in Sum: 150 Years of Mathematics at Harvard (1825-1975)
Steve Nadis, Shing-Tung Yau
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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.
undergraduate of his generation to comprehend” Peirce’s higher mathematical demonstrations.36 Like Peirce, Hill believed that “our best Professors are so much confined with the onerous duties of teaching and preparing lectures that they have no time nor strength for private study and the advancement of science and learning.” The system’s failing was especially pronounced in mathematics education, Hill said, owing to the “inverted method” adopted in so many schools of “exercising the memory,
Abbott Lawrence Lowell received a letter from the physician Roger Lee, which said: “I quite agree that in the case of Professor Osgood it would be well to ask him to retire on account of age as soon as it is decent.”63 Lowell wrote to Osgood two months later asking for his resignation at the end of the academic year. Lowell cited a provision 53 54 A H I S T O RY I N S U M in the university’s bylaws whereby “any professor shall retire on his pension at sixty-six if requested to do so.” Osgood
art or music piece, O is the piece’s “order” (which relates to how harmoniously its parts fit together), and C is its complexity. His interest in analyzing art and music had been longstanding, according to Morse, and Birkhoff gave a hint as to where that interest sprang when a musician asked him about the point of studying mathematics. “One should study mathematics,” Birkhoff replied, “because it is only through mathematics that Nature can be conceived in harmonious form.”55 In addition to
in World War I, returning to the university in 1919 as a Benjamin Peirce Instructor. He then taught for a few years at Cornell and Brown, rejoining the Harvard faculty in 1926. A year before coming to Harvard, in his 1925 paper “Relations between the Critical Points of a Real Function of n Independent Variables,” Morse laid out the first installment of a new mathematical theory that would become his life’s work.5 He elaborated on this theme, laying the foundations for what is now called Morse
their mathematical skills. These times were apparently etched in stone, or etched into the school’s bylaws, which stated that the hours were not subject to change “unless experience shall show cause to alter.”7 In the first one hundred or so years, mathematics instructors, who held the title of tutors, had little formal training in the subject—consistent with the general sentiment that the subject itself hardly warranted a more serious investment. Students, similarly, had to demonstrate