AWM Book Review

WHAT I READ ON MY SUMMER VACATION

Women in Mathematics: The Addition of Difference

Claudia Henrion,Indiana University Press, Bloomington 1997. xxxi+293pp. ISBN 0-253-33279-6 (cloth), $39.95; ISBN 0-253-21119-0 (paper), $16.95.

A Beautiful Mind: A Life of John Forbes Nash, Jr.

Sylvia Nasar, Simon and Schuster, New York 1998. 459pp. ISBN 0-684-81906-6 (cloth), $25.00.

From: AWM Newsletter, September/October 1998.

Reviewed by: Marge Murray, Book Review Editor, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123; email: murray@calvin.math.vt.edu.

At first glance, the two books under review would seem to have little in common. Claudia Henrion is a mathematician and educator, and her Women in Mathematics is an exploration of "the ideology of the mathematics community" and an examination of "the impact of this ideology on women" by means of a close examination of the lives and careers of eleven contemporary women mathematicians (xvii). Sylvia Nasar is an economics reporter for The New York Times, and her Beautiful Mind is a biography of John Nash, the mathematician who won the 1994 Nobel memorial prize in economics for his work in game theory. But in fact, there are close affinities between the two books, as I hope to make clear in what follows.

Let me begin by saying that each book is deserving of a review in itself; I must apologize both to the authors and to the readers of this Newsletter for the fact that the two books are being reviewed together. Moreover, I can do little to improve upon Ann Hibner Koblitz' very thorough featured review of Henrion's book in the May 1998 AMS Notices, which I recommend to any reader seeking a thorough analysis of its strengths and shortcomings from an historian's perspective.

Among the chief aims of Henrion's book is to elucidate and critique some of the mathematical community's (often unspoken) assumptions about how mathematics is done. In particular, Henrion emphasizes the assumption that mathematics is done in isolation from other people; that mathematicians are normally white and male; that mathematics is an activity for the young; that mathematics exists in isolation from politics and political considerations; that mathematical knowledge is objective and absolute. Unfortunately, Henrion neither explains the historical origins of this ideology, nor does she make use of historical arguments to critique its apparently timeless validity. Yet many of her underlying assumptions about the conduct and values of scientific and mathematical inquiry in the United States date back to the 1930s and 1940s, and gathered momentum during World War II and the Cold War that followed. The historical context is indispensable to an understanding of the functioning of the mathematical community during that period --- as well as to an understanding of how the community functions now.

Curiously, Sylvia Nasar's book provides a good deal of the historical context for the ideology that Henrion describes, as well as some basis for its critique. On the surface, A Beautiful Mind is the often tragic but ultimately redemptive story of John Nash who, after making substantial contributions to mathematics and economics at an early age, was diagnosed as a schizophrenic and disappeared from public view for nearly thirty years. During his sixties, however, Nash made a partial recovery and returned to intellectual activity, the Nobel prize providing him at last with the recognition he craved. But at another level, Nasar's book can be read not simply as a portrait of an individual mathematician, but also as a fine-grained account of the mathematical community and its ideology, particularly in the 1940s and 1950s.

Born in 1928, Nash spent the late 1940s and the entire decade of the 1950s in and around Princeton, MIT, NYU, and RAND. At this time and in these places, the mathematical ideology to which Henrion refers came to full flowering; Nash himself was among the prime examplars of the mythology of youthful, competitive, male mathematical genius. Because Nasar is an outsider to the mathematical community, she presents the ideology as well as the mystique of Nash and his contemporaries uncritically, with a reporter's keen sensitivity to detail. What emerges from her account is a clear sense of the manner in which, in the prosperous postwar era, mathematics became a means by which socially awkward, intellectually gifted young men could attain power and prestige.

Nasar's book illuminates the ideology of the American mathematical elite in the 1950s. But, inasmuch as Nasar is describing the conduct of mathematics in various hothouse environments of the period, it does not accurately represent the variety and diversity of mathematical life during that difficult decade. Henrion's portraits of Mary Ellen Rudin and Marian Boykan Pour-El, roughly contemporary with Nash, underscore the fact that the mathematical community, even during the most overtly sexist periods of its history, has made room for a variety of ways of being and doing mathematics. Indeed, I agree with Ann Hibner Koblitz that Henrion's profiles of women mathematicians are the greatest strength of her book.

Interestingly, Henrion's and Nasar's books share a common failing: neither gives a clear sense of the ways in which the ideology of the mathematical community continues to change over time. The general educated reader, to whom Nasar's book is directed, can easily come away with a sense that the mathematical ethos of the 1950s continues to this day. The target audiences for Henrion's book --- scholars in mathematics, women's studies, and social studies of science --- can just as easily come away with the sense that the ideology she describes is indeed timeless and, save for the efforts of a few renegade female (and perhaps male) mathematicians, essentially static.

Still, separately and together, these two books should give rise to provocative discussions about the nature of the mathematical and scientific communities; the value of diverse points of view; and the future of mathematics in the face of rapid technological, political, and demographic change. Moreover, inasmuch as both books examine how difficult it can be for both men and women to successfully integrate their mathematical and personal lives, these books should stimulate important conversations about how one might live a life that is both mathematically productive and personally fulfilling.