Book Review A History in Sum

Reviewed by Steve Batterson

mathematics.” Spoiler alert: If you would like to A History in Sum: 150 Years of Mathematics at make your own selections, the names are listed two Harvard (1825–1975) paragraphs below. In fleshing out these lives, the Steve Nadis and Shing-Tung Yau authors rely on interviews and published material Harvard University Press, October 2013 280 pages, $39.95 rather than archival sources. As in their first book, ISBN-13: 978-06747-250-03 The Shape of Inner Space, Nadis and Yau set out to make deep mathematics accessible. This time, instead of string theory, the topics range over the Mathematicians may be surprised by 1982 Fields various breakthroughs of their stars. Medalist Shing-Tung Yau’s collaboration with sci- Some readers will have opinions on the merits ence writer Steve Nadis on a history of the Harvard of a comprehensive departmental history versus mathematics department. Perhaps anticipating singling out its greatest men (at Harvard they are some bewilderment, Yau begins his portion of all men). I welcome both approaches as valuable the preface with a justification of why history is additions to the literature, particularly in view important to mathematics. For the purposes of of the distinction of the Harvard and Berkeley this review, I regard historical value as an axiom. A History in Sum joins Cal Moore’s Mathematics departments. In the interest of full disclosure, at Berkeley in the genre of book-length histories I need to state that I received honoraria from of American mathematics departments. Although Harvard University Press for commenting on the both volumes are dominated by biographies of manuscript at two stages of its development. university faculty, their underlying methodologies The division of labor between the two authors and objectives are very different. Moore wrote is not discussed beyond that the initiative arose what might be classified as a traditional history. He from Yau. One assumes that Yau selected the excavated the Berkeley archives and produced a names. His bona fides confer special interest on detailed record of the scholarly advancement of the what, in itself, is an intriguing list: Benjamin Peirce, department since the founding of the University Osgood, Bôcher, G. D. Birkhoff, Morse, Whitney, of California in 1868. His narrative includes the Mac Lane, Ahlfors, Mackey, Gleason, Zariski, Brauer, basic vitae of every faculty member and much Bott, and Tate. Yau acknowledges an element of more, analyzing changes in the department over subjectivity in making difficult decisions about the years. whom to include. While he understandably does not Nadis and Yau focus on the stories of Harvard discuss specific omissions, consider some of the personnel making pioneering mathematical dis- Harvard mathematicians who are not featured in coveries. A History in Sum features biographies of the book. Fields Medalists Mumford and Hironaka, fourteen Harvard faculty, from the period 1825– whose careers may have been regarded as too 1975, “that made the greatest contributions to late, get some attention as students of Zariski. Joseph Walsh and Marshall Stone receive a mere Steve Batterson is professor of mathematics and computer science at Emory University. His email address is sb@ paragraph apiece, comparable to Moore’s coverage mathcs.emory.edu. of Annie Dale Biddle Andrews, an obscure Berkeley DOI: http://dx.doi.org/10.1090/noti1133 instructor terminated in 1933. Dunham Jackson,

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André visitor, te ra coas ase hte preferred Whitney Hassler scholars, mathe- great with doing other interaction on thrived to Zariski Whereas approaches matics. contrasting trate Grothendieck. Alexander and Serre as Mumford, David and Artin, Heisuke Michael students 1950s Hironaka, his late included the milieu Zariski In the geometry. algebraic for distinguished center in bringing and students Jewish strong tenured attracting By faculty. first Harvard the the on mathematician became Zariski Brazil, another he with There discussions Paulo. stimulating São in in engaged professor exchange an as needed. algebraic Zariski the that of structures some on year lectures Bryn same delivering from Mawr, Princeton that to In commuted Noether 1934–1935. Emmy visit for to Zariski institute for the support full provide to agreed h eiso hi hoes yn hmtogether them Tying theorems. their of merits the to tendency a qualities. have personal airbrush tributes Memorial faculty. 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Number , Their . illus- 6 is their link to Harvard. The strength of the A  M  S Harvard mathematics department, going back to Ahlfors and Birkhoff, is well known. The careers of Benjamin Peirce, W. F. Osgood, and Maxime Bôcher demonstrate that, with the exception of the ten years from Peirce’s death (1880) to the appointment of Osgood (1890), the university Selected Papers of V. S. faculty has included leading mathematicians since Varadarajan 1831. Indeed, Harvard merits consideration with Johns Hopkins and the University of Chicago as the Volumes 2 and 3 first academic home for mathematical scholarship Donald G. Babbitt and Ramesh Gangolli, K. R. Parthasarathy, Indian Statistical Institute, New Delhi, India, Enrico G. Beltrametti in the United States. and Gianni Cassinelli, University of Genova, Italy, Rita Fioresi, Although the authors focus on mathematics Università di Bologna, Italy, and Anatoly N. Kochubei, National at Harvard, a connection to the university is Academy of Sciences of Ukraine, Kiev, Ukraine, Editors not necessary for enjoyment of the book nor is The current volumes contain the papers on fundamental questions of individual and families of meromorphic differential equations that are treated by a new group any special knowledge of the areas explored. A theoretic and functional approach; papers on representation theory of Lie groups; papers on foundations of physics, supersymmetry, and P-adic aspects of quantum History in Sum should find an audience among physical theories; papers on analysis, especially oscillatory integrals, on semi-simple mathematicians from two broad classes: those who lie groups, their conjugacy classes, and their flag manifolds; and finally, several review articles, both personal and mathematical, on a number of the above topics. enjoy biography and those who would like to gain Hindustan Book Agency; 2013; 1366 pages; Hardcover; ISBN: 978-93-80250-57-1; a nontechnical flavor of major developments in List US$165; AMS members US$132; Order code HIN/65 their science. Publications of Hindustan Book Agency are distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

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