2012 Whiteman Prize

Joseph Warren Dauben received the 2012 AMS them to early Western mathematics and make them Albert Leon Whiteman Memorial Prize at the 118th understandable to the modern reader. “Chinese Annual Meeting of the AMS in Boston in January mathematics,” his contribution to The Mathemat- 2012. ics of Egypt, Mesopotamia, China, India, and Islam (Princeton University Press, Princeton, 2007), is Citation the fruit of twenty years of scholarship and, at The American Mathematical Society is pleased to nearly 200 pages, is a book in its own right. Dauben award the Albert Leon Whiteman Prize to Joseph studies the history of modern Chinese mathemat- Warren Dauben for his contributions ics as well; see, for example, his chapter “Modern to the history of Western and Chinese science emerges in China” in Mathematics Un- mathematics and for deepening and bound: The Evolution of an International Math- broadening the international math- ematical Research Community, 1800–1945 (History ematical community’s awareness of Mathematics, 23, Karen Hunger Parshall and and understanding of its history and Adrian L. Rice, editors, American Mathematical So- culture. “In truth mathematics can ciety, Providence, RI; London Mathematical Society, be called the Pleasure Garden of the London, 2002). He is an elected Honorary Professor myriad forms, the Erudite Ocean of of the Institute for the History of Natural Science the Hundred Schools of Philosophy,” (a branch of the Chinese Academy of Sciences) and said the sixteenth-century mathema- lectures there regularly. tician Xu Guangqi. Joe Dauben’s work In Writing the : Its His- illuminates his epigram. torical Development (Sci. Networks Hist. Stud., Dauben’s first book, Georg Can- 27, Birkhäuser, Basel, 2002), Dauben and coeditor tor: His Mathematics and the Phi- Christoph Scriba engage historians of mathemat- ics around the world to show how the practice of Joseph W. Dauben losophy of the Infinite (Harvard Uni- versity Press, Cambridge, MA, 1979; writing history of mathematics has varied from reprinted, Princeton University Press, country to country and era to era and how this Princeton, 1990), is a clear, readable, detailed, historiography is intertwined with the philo- richly textured history of Cantor’s development sophical, scientific, and industrial demands of of transfinite numbers and, at the same time, an time and place. In the United States, the history insightful but nonreductive account of the com- of mathematics, once an excellent but eclectic plex and difficult personality that brought this collection of teaching tools and postretirement revolution about. His second biography, Abraham projects, has in the last decades become an inte- Robinson: The Creation of Nonstandard Analysis, gral component of the mathematical community, A Personal and Mathematical Odyssey (Princeton with well-attended sessions at major meetings. University Press, Princeton, 1995), is another Joe Dauben has spurred this professionalism by near-impossible feat of scholarship and exposi- his scholarly example and through his service tion. Dauben traces Robinson’s nonstandard path to the profession, which includes organizing from his birthplace in Germany to his death in international workshops and symposia and editing New Haven, via Palestine, Paris, London, Toronto, Historia Mathematica for a decade. Jerusalem, and Los Angeles, again intertwining the Like his list of published articles, the list of Joe mathematician and his mathematics. Dauben’s honors is long. We are proud to add the While writing Abraham Robinson, Dauben Whiteman Prize to it. began a study of “Ten Classics of Ancient Chinese Biographical Sketch Mathematics”, a 656 CE edition of texts taught throughout Chinese history, in order to relate Joseph W. Dauben is Distinguished Professor of History and the History of Science at Herbert H. DOI: http://dx.doi.org/10.1090/noti828 Lehman College and a member of the Ph.D. Program

572 NOTICES OF THE AMS VOLUME 59, NUMBER 4 in History at the Graduate Center of the City had himself been a student at USC and was the University of New York. He is a fellow of the New reason I had applied there as one of my choices for York Academy of Sciences, a membre effectif of graduate school. But, having grown up in south- the International Academy of History of Science, a ern California, the offer Harvard made to pursue corresponding member of the German Academy of my doctorate there in history of science proved Sciences Leopoldina, and a member of the Society irresistible, and in the fall of 1966 I found myself of Fellows of the American Academy in Rome. He on the East Coast, in Cambridge, where there was has been editor of Historia Mathematica, an inter- a lively, if small but in retrospect remarkable, national journal for the history of mathematics, concentration of historians of mathematics. The and chairman of the International Commission Department for History of Science, one of the first on the History of Mathematics. He is the author in the country, had just been established, and I was of Georg Cantor, His Mathematics and Philosophy among the earliest groups to join the new depart- of the Infinite (Harvard University Press, Cam- ment, along with my friend, colleague, and fellow bridge, MA, 1979; reprinted, Princeton University historian of mathematics Wilbur Knorr. Wilbur Press, Princeton, 1990) and Abraham Robinson: and I were very fortunate to have been trained by, The Creation of Nonstandard Analysis, a Personal among others, John Murdoch and Judith Grabiner, and Mathematical Odyssey (Princeton University who prepared us with tutorials for just the two Press, Princeton, 1995), both of which have been of us for our oral examinations prior to working translated into Chinese. Among his most recent on our Ph.D.’s, which I did under the direction of publications is the monographic study of one of Erwin Hiebert and Dirk Struik. While at Harvard, the most ancient works of Chinese mathematics, I was also fortunate to have worked with Richard “Suan shu shu. A book on numbers and compu- Brauer, who took an interest in my thesis on Can- tations. English translation with commentary” tor and whose own memories of mathematics in (Archive for History of Exact Sciences 62 (2008), Germany were always helpful to me in getting right no. 2, 91–178). A graduate of Claremont McKenna the historical sense of the times in which Cantor College, magna cum laude, in mathematics and of had lived, especially his later years. If Brauer said Harvard University (A.M. and Ph.D.) in history of something I had written sounded correct to him, science, Dauben has been a member of the Insti- I felt it must be pretty close to the mark. Later, tute for Advanced Study (Princeton) and Clare Hall another Harvard mathematician, Garrett Birkhoff, (Cambridge University), where he was affiliated would likewise prove very helpful when the subject with the Needham Research Institute. He has been of my research turned to a biography of Abraham the recipient of a Guggenheim Fellowship, Senior Robinson. Birkhoff had known Robinson and was NEH and ACLS Fellowships, and was named Out- interested in the historical implications of non- standing Teacher of the Year at Lehman College in standard analysis. Wim Luxumburg at Caltech and 1986. He is an honorary member of the Institute for George Seligman at Yale were also colleagues and History of Natural Sciences of the Chinese Acad- good friends of Robinson and likewise mathemati- emy of Sciences, where he was the Zhu Kezhen cians to whom I am grateful for their reading of Visiting Professor in spring of 2005. In 2010 he the history I was writing. was Visiting Research Professor at the Institute for This is all by way of saying that, for historians Humanities and Social Sciences at National Chiao- of mathematics, our best audiences and most Tung University in Hsinchu (Taiwan). valuable collaborators are our mathematician colleagues. In the course of my career as a his- Response from Joseph Warren Dauben torian of mathematics, I have also learned the Albert Leon Whiteman was a mathematician with craft from many of my colleagues, who have been a passion for number theory and an abiding inter- both inspirational and supportive. I was indeed est in the history of mathematics. He was Hans fortunate to have several of what in Germany is Rademacher’s first student at the University of called the Doktorvater, beginning with my mentor Pennsylvania and a Benjamin Peirce instructor at at Harvard, I. Bernard Cohen, whose own interest Harvard before taking up a position in 1948 at the in history of mathematics included the work of University of Southern California, where he spent Isaac Newton but also the great revolution in the rest of his career. I might have been one of his computers that led him to serve as IBM’s chief graduate students, for USC was one of the universi- historical consultant. That led to several summers ties where I was accepted to continue as a graduate when both Wilbur Knorr and I, among a number student in mathematics after I had completed my of graduate students, were employed to work for undergraduate degree in 1966 at Claremont McK- IBM on a massive history of computing database enna College in southern California. I had studied that Cohen was overseeing. mathematics there with John Ferling, Granville In Berlin, when I was there for a year doing archi- Henry, and Janet Myhre and wrote my senior thesis, val research for my dissertation on Georg Cantor which later would prove to be especially useful, and the origins of transfinite set theory, Kurt R. as it turned out, on nonstandard analysis. Ferling Biermann, director of the Alexander von Humboldt

APRIL 2012 NOTICES OF THE AMS 573 Forschungsstelle at the Deutsche Akademie der York for a second doctorate in history of science Wissenschaften in what was then East Berlin, took after having already completed a Ph.D. in math- me under his wing, as did Herbert Meschkowski at ematics was David Rowe, then Horng Wann- Sheng, the Freie Universität and Christoph Scriba at the and most recently, Xu Yibao. At the moment, I have Technische Universität in West Berlin. The German yet another graduate student from Taiwan, Chang circle of historians of mathematics kindly invited Ping-Ying, who is working on a history of the Su- me to their annual meetings at the Mathematisches anxue (College of Mathematics) in the Qintianjian Forschungsinstitut at Oberwolfach in the Black For- (Bureau of Astronomy) in the early Qing Dynasty, est, where Joseph Ehrenfried Hofmann, especially a reminder of the fact that in virtually all cultures known for his research on Leibniz, had established in all parts of the world, mathematicians have sig- the Problemgeschichte der Mathematik seminars. nificant roles to play, not just in the advancement Over the years meetings there with Christoph of the theoretical understanding of the subject but Scriba, Menso Folkerts, Ivo Schneider, Eberhard in a wide variety of applications. Knobloch, Herbert Mehrtens, among many others, In addition to the very great extent to which introduced me to the grand tradition of history of the American Mathematical Society and the Math- mathematics in Germany. Later Christoph Scriba ematical Association of America have furthered and I would codirect, with and the history of mathematics through the invited Jeanne Peiffer, a group project for the International sessions on history, which usually run a full two Commission of the History of Mathematics that days at the annual joint meetings (for which over resulted in a collaborative historiographic study the years I’ve served as co-organizer with, at vari- bringing colleagues from literally all parts of the ous times, David Zitarelli, Karen Parshall, Victor world together to write a history of the discipline. Katz, Patti Hunter, and Deborah Kent), the History Also among those to whom I owe so much, begin- of Science Society in recent years has also shown ning with the help and encouragement he offered increasing interest in the history of mathematics. me as a graduate student, is Ivor Grattan-Guinness, There Karen Parshall and Albert Lewis have been whose own early work on Georg Cantor proved instrumental, along with support offered by Harry extremely helpful to me, especially through the Lucas, in establishing a Forum of the History of strategic suggestions Ivor was willing to offer at Mathematics that we hope will serve to increase the time to a fledgling graduate student; but over further the prominence of history of mathematics the years since, his critical and editorial eye has at HSS annual meetings. always been welcome, as well as the various proj- In retrospect, I have much to be thankful for ects on which we have worked together. in a career that has brought me into touch with In fact, throughout my career, working with mathematicians and historians the world over, mathematicians and historians in different parts many of whom I consider not just colleagues but of the world has been the most rewarding and good friends, including the students I have been inspirational aspect of collaborative research. privileged to have at the Graduate Center of the This has certainly been true of the undertaking I City University of New York. But it is my home began nearly twenty-five years ago, in 1988, when institution, Herbert H. Lehman College, to which I was invited to spend six months in China under I must say a special thank you for the resources a program jointly sponsored by the Chinese Acad- and encouragement it gives to faculty, especially emy of Sciences and the U.S. National Academy for their research and participation in confer- of Sciences. I spent several months that spring ences and projects involving the larger academic in Beijing at the Institute for History of Natural community of scholars. It was Lehman that gave Sciences, where I joined the seminar on history of financial support and released time from teach- Chinese mathematics being taught by Du Shiran. ing when Esther Phillips and I served as editors of It was there that I met Guo Shuchun and Liu Dun, Historia Mathematica following the sudden and un- two historians of mathematics who, along with expected death of its founding editor, Kenneth O. Lam Lay Yong in Singapore and Horng Wann-Sheng May. More recently, Lehman helped make possible in Taiwan, have also been those from whom I a year at the Research Center for Humanities and have learned the history of Chinese mathematics. Social Sciences at National Chiao-Tung University Wann-Sheng, in fact, not long after I returned to in Hsinchu, Taiwan. There, with few obligations New York from Beijing, was the first of my Chinese apart from my own research, I spent all of 2010 graduate students, and the other joy of teaching completing a translation with critical commentary is the opportunity it provides for working with of the Nine Chapters on the Art of Mathematics (one especially able students. Although I have not had of the Ten Classics of Ancient Mathematics). The many graduate students, those with whom I have Nine Chapters, including its commentaries, is the worked have been a pleasure to mentor, and in the compendium of mathematics from ancient China process, I am convinced that I learn as much from on which I have been fortunate to work with my them as I hope they have learned from working colleagues Guo Shuchun in Beijing and Xu Yibao with me. The first student to find his way to New in New York. This collaborative effort would not

574 NOTICES OF THE AMS VOLUME 59, NUMBER 4 have been possible were it not for the joint support sincere appreciation, and on behalf of historians of the City University of New York, Chiao-Tung of mathematics everywhere, my heartfelt thanks University in Taiwan, and the Institute for History as well to Mrs. Sally Whiteman for establishing of Natural Sciences in Beijing. this outstanding memorial for her husband, Albert What sets the history of mathematics apart Leon Whiteman. from the history of science generally is that it is not an arcane history about past theories that About the Prize have been discarded, forgotten as failed attempts The Whiteman Prize is awarded every three years to understand the workings of nature, but instead to recognize notable exposition and exceptional the history of mathematics is a living history. In the scholarship in the history of mathematics. The nineteenth century Weierstrass recommended that prize was established in 1998 using funds donated his students read the classics of the past, for such by Mrs. Sally Whiteman in memory of her husband, works might well contain ideas and methods that the late Albert Leon Whiteman. The prize carries a could still prove useful, even inspirational, to cur- cash award of US$5,000. rent mathematical research on the frontiers of the The Whiteman Prize is awarded by the subject. It is for this reason that mathematicians, AMS Council acting on the recommendation more than any other practitioners among the sci- of a selection committee. For the 2012 prize, ences, have a very real interest in their history—not the members of the selection committee were just to remember the past, but to use it. For the Robin Hartshorne, Marjorie Senechal, and Wil- tangible support and visibility that awards like the liam C. Waterhouse. Previous recipients of the Whiteman Memorial Prize provide for the subject, Whiteman Prize are Thomas Hawkins (2001), Har- historians of mathematics can truly be grateful, old M. Edwards (2005), and Jeremy J. Gray (2009). and at this moment in particular, none more than I. To the AMS Council and to the members — Elaine Kehoe of the selection committee, I want to express my Award for Distinguished Public Service

William McCallum received the 2012 Award for Principal Investigator on a Mathematics and Sci- Distinguished Public Service at the 118th Annual ence Partnership grant. Meeting of the AMS in Boston in January 2012. However, his most significant recent activities have also been the most distinctive. He is the Citation founding Director of the Institute for William McCallum is University Distinguished Mathematics and Education (IME) at Professor and Head of the Mathematics Depart- the University of Arizona and is cur- ment at the University of Arizona. In recent years, rently director of its Advisory Com- McCallum has shown extraordinary energy in pro- mittee. This Institute was founded moting improvement of mathematics education, explicitly on the principle that to and he has been almost ubiquitous in organiza- deal effectively with issues of math- tions devoted to mathematics education. He has ematics education requires com- served as chair of the Committee on Education of munication and cooperation among the AMS and as chair of CBMS. He is a member of teachers, mathematics education the International Design Committee for the Klein researchers, and mathematicians. In Project, an effort of the International Commission dozens of events over the past five on Mathematics Instruction and the International years, many people from all three Mathematical Union to produce a set of narratives groups have met for mutually pro- or “vignettes” about contemporary mathematics to ductive activities under the auspices William McCallum educate and inspire today’s high school teachers of IME. in the way that Felix Klein’s lectures and books Most recently, he was one member of on “Elementary Mathematics from an Advanced the three-person writing team selected by the Coun- Standpoint” did 100 years ago. He has also been cil of Chief State School Officers and the National Governors Association to orchestrate and execute DOI: http://dx.doi.org/10.1090/noti822 the production of the Common Core State Math-

APRIL 2012 NOTICES OF THE AMS 575