<i>A History in Sum: 150 Years of Mathematics at Harvard, 1825-1975</i>, by Steve Nadis and Shing-Tung Yau

A History in Sum: 150 Years of Mathematics at Harvard, 1825-1975, by Steve Nadis and Shing-Tung Yau. Cambridge, Harvard University Press, 2013. xviii, 249 pp. $39.95 US (cloth). This lively and accessible book traces the lives and work of some of the most eminent and influential mathematicians associated with Harvard over the 150year period from 1825 to 1975. As the authors, science writer Steve Nadis and Harvard mathematician Shing-Tung Yau acknowledge, those dates are, however, somewhat arbitrary. Benjamin Peirce (1809-1880), arguably the first research mathematician to serve at Harvard, entered what was then Harvard College as a member of the 1825 freshman class and began a career on the faculty there six years later that would end only with his death. By 1975, Harvard had established itself as one of the leading mathematics departments internationally both by fostering American-born mathematical talents and, ultimately, by opening its doors to foreign-born mathematicians of recognized strength. The stories of thirteen mathematicians shape a narrative that is both biographical and mathematical. Although the seventeenth- and eighteenth-century history of mathematics at Harvard is very briefly sketched, the book opens in the nineteenth century with the story of Benjamin Peirce, a home-grown scholar who personally embraced the research ethos at a moment in the history of American higher education when that ethos was not widely shared. Peirce, in fact, was a member of a loosely knit group at midcentury that worked to orient American science toward research and publication and, more generally, toward professionalization as it had been institutionalized in Europe. It is a missed opportunity that the authors failed to contextualize Peirce within these broader trends within the history of science in the United States. It would have made a rich story even richer while also providing meaningful historical explanations for why it was actually perfectly natural that [t]he 'publish or perish' ethic, which came to be so dominant by the closing decades of the twentieth century and with which the authors are well aware, evidently, had not yet taken hold (p. 7) in mid-nineteenth-century America. In the telling of their story, the authors fall more than once into this trap of judging and interpreting the past by the present. From Peirce (whose son, the mathematician, geodesist, and philosopher, Charles Sanders Peirce, is incorrectly portrayed in the images that appear between pages 140 and 141 of the book), the narrative moves to the turn of the twentieth century when William Fogg Osgood (1864-1943) and Maxime Bocher (1867-1918) brought their German training and research ideals back to a Harvard by then under the leadership of Charles Eliot. Over the course of his forty years as president, Eliot labored to transform colonial Harvard College into modern Harvard University, largely in response to developments in American higher education taking place at the Johns Hopkins University and somewhat later at the University of Chicago and elsewhere. Osgood and Bocher had both studied at Gottingen University in the 1890s under the leading German mathematician, Felix Klein, and had both continued actively to pursue and to publish the fruits of their mathematical labours after their return to American shores. They, but most successfully Bocher, worked to reorient mathematics at Harvard toward research and the training of future researchers. …

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