Thomas Hawkins the First Whiteman Prize First of His Presentations to an International Was Awarded at the Joint Math- Congress of Mathematicians (ICM) in 1974

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2001 Whiteman Prize

The Albert Leon Whiteman book on Lebesgue’s Theory of Integration: Its Prize was established in 1998 Origins and Development (Madison and London: using funds donated by Mrs. University of Wisconsin Press, 1970). Now a Sally Whiteman, in memory of recognized classic in the field, this work, like all of her husband, the late Albert Hawkins’s subsequent research, is characterized Leon Whiteman. Mrs. White- by its historical depth and mathematical percep- man requested that the prize tiveness. be established for notable ex- After 1970, however, Hawkins gradually shifted position on the history of his research from the history of nineteenth- and mathematics. The ideas ex- early twentieth-century analysis to the develop- pressed and the new under- ment of group representation theory and Lie groups. standings embodied in the ex- This new line of inquiry began with papers on the position recognized by the representation theory of finite groups, which cul- Whiteman Prize should reflect minated with the paper “New light on Frobenius’ exceptional mathematical creation of the theory of group characters” (1974). scholarship. The $4,000 prize By that time this work had led to research on the is awarded every four years. history of matrix theory, as can be seen from the Thomas Hawkins The first Whiteman Prize first of his presentations to an International was awarded at the Joint Math- Congress of Mathematicians (ICM) in 1974. In ematics Meetings in New Orleans in January 2001 Vancouver he discussed the theory of matrices in to THOMAS HAWKINS. the nineteenth century and showed that more is The Whiteman Prize is awarded by the AMS owed to Weierstrass, and less to Cayley, than then- Council acting through a selection committee standard texts would have it. This insight led him, whose members at the time of this award were via his paper “Wilhelm Killing and the structure of Joseph W. Dauben, Jeremy J. Gray (chair), and Lie algebras” (1982), to investigate the tangled Karen Hunger Parshall. The text that follows history of the theory of linear representations of contains the committee’s citation, a biographical semi-simple Lie groups, the subject of his second sketch, and a response from Thomas Hawkins ICM address at Berkeley in 1986. Since then he has upon receiving the prize. written extensively on the history of Lie groups. In particular, he has traced their origins to work in Citation the 1870s on differential equations and contact In awarding the first Albert Leon Whiteman Prize transformations in which Lie applied both Poisson to Thomas Hawkins, professor of mathematics at brackets and the Jacobi identity to study the inte- Boston University, the American Mathematical gration of partial differential equations. In “Jacobi Society recognizes an outstanding historian of and the birth of Lie’s theory of groups” (1991), mathematics whose current research and numer- Hawkins argued convincingly that the idée fixe ous publications display the highest standards of guiding Lie’s work was the development of a Galois mathematical and historical sophistication. theory of differential equations. Another paper, Hawkins began his career in the history of math- “Hesse’s principle of transfer and the representa- ematics with the publication of a groundbreaking tion of Lie algebras” (1988), found the roots of Élie

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Cartan’s 1913 paper on the construction of all supported by both historical and mathematical irreducible representations of a complex semi- institutions. With the financial support of the simple Lie algebra in nineteenth-century algebra American Council of Learned Societies, he spent and geometry. Hawkins has also studied Killing’s 1969–70 as a guest of the Forschungsinstitut für work in detail, debunking, in particular, the in- Mathematik at the Eidgenössische Technische flated claims as to the influence of Klein’s Erlanger Hochschule (ETH) in Zürich. During 1980–81 he Program at the time of its appearance. In drawing was a visiting scholar in the Department of History his historical conclusions, Hawkins has relied not of Science at Harvard University, with financial only on the published mathematical record but support provided by the National Science Founda- also on collections of letters and other archival tion program in history and philosophy of science. sources. His reading of these varied sources has, The School of Mathematics of the Institute for moreover, been guided by a sure sense of the Advanced Study in Princeton provided him with mathematical connections involved, even when, support as a visiting member during 1988–89, as has often been the case, these have been lost and and the Dibner Institute for History of Science and forgotten as a result of the subsequent growth of Technology at the Massachusetts Institute of the subject. Technology did the same during 1996–97, when All of this work has culminated most fruitfully most of his book on the history of Lie groups in the publication of his long-awaited book The was written. In 1997 he was awarded the Chauvenet Emergence of the Theory of Lie Groups: An Essay Prize of the Mathematical Association of America in the History of Mathematics 1869–1926 (New for his paper “The birth of Lie’s theory of groups” York: Springer-Verlag, 2000). This study treats in (Math. Intelligencer 16 (1994), no. 2, 6–17). great depth the work of Sophus Lie, Wilhelm Killing, Response Élie Cartan, and Hermann Weyl as it highlights the fascinating interaction of geometry, analysis, As one who has been researching the history of mathematical physics, algebra, and topology mathematics for more than thirty years, it is a in the late nineteenth and early twentieth centuries. great honor for me to become the first recipient It displays to the full Hawkins’s deeply held belief of the Whiteman Prize. The creation of this prize is particularly meaningful to me as a further that mathematical understanding grows when manifestation of the importance the AMS attaches the underlying motivations and the original, to the historical study of mathematics. informal, intuitive conceptions are uncovered Thirty-five years ago, however, when I commit- and illuminated. It also interweaves the critical hu- ted myself to a career in history of mathematics, man dimension into the story through extensive there was in this country no such recognition of quotation of the mathematicians’ private corre- historical work by professional mathematical spondence. societies. In deciding to pursue a career in this Hawkins’s many contributions to the history of area, I realized I was facing the prospect of a lonely mathematics have already won him much deserved and not quite respectable existence within the recognition. In addition to twice addressing the In- community of mathematicians, the professional ternational Congress of Mathematicians, he received group to which I felt the closest affinity. I am happy the Chauvenet Prize for mathematical exposition to report that my dire expectations proved to from the Mathematical Association of America in be unfounded. After leaving Wisconsin I was 1997. In presenting the first Albert Leon Whiteman encouraged by the growing interest a number of Memorial Prize to Thomas Hawkins, we acknowl- distinguished mathematics departments showed in edge a body of scholarship characterized by my work through their unsolicited invitations to breadth and coherence, clarity and sensitivity to speak about it. Among the many such departments, historical detail, and depth of insight. Hawkins’s I want to mention in particular those at the work has truly transformed our understanding of University of Chicago and Yale University, where I how modern mathematics has evolved. have been invited back many times to talk about my latest discoveries. In addition, over the years Biographical Sketch many first-rate mathematicians have respectfully Thomas Hawkins received a Ph.D. degree with a encouraged me in my work or have assisted me by joint concentration in mathematics and history of reading over preliminary drafts of papers and by science from the University of Wisconsin-Madison sharing their expertise, thereby helping me to avoid in 1968. After passing the Ph.D. qualifying exami- countless pitfalls as well as to explore connections nations of both departments, he wrote a dissertation I would have otherwise missed. To all the mathe- on the origins of the theory of Lebesgue integration, maticians who in one or more of the above- which was published as a book in 1970. After a few mentioned ways have supported and assisted my years teaching at Swarthmore College, he accepted work, I hereby extend my heartfelt thanks. a position in the mathematics department at Boston University, where he has remained. Over the years his work on the history of mathematics has been

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