Until recently, *Women of Mathematics: A Biobibliographic Sourcebook*, 1987, edited by Louise Grinstein and Paul Campbell (also from Greenwood Press), and Teri Perl's *Women, Numbers and Dreams* were practically the only two reference works on women in mathematics. This new book complements the other two by emphasizing the human element. The result is a valuable book for and about women in mathematics at a level suitable for high school and early college students that celebrates the diversity present in the community of women mathematicians.

The goal of the editors, stated on page xv, is admirable: to encourage more girls into mathematics and to spark enthusiasm for the field in all students. To this end, they have collected biographical information on 59 women mathematicians, spanning the last 2000 years. The emphasis, however, is on contemporary women mathematicians: of the 59, 40 are currently living and working in the field of mathematics or mathematics education in the US or in Europe. Much of this material comes from personal interviews, and thus goes beyond each woman's mathematics to discuss the person behind the mathematics.

The essays are a delight to read. Each gives a very human and encompassing picture of the whole woman -- as mathematician, teacher, mother, wife or partner. Each one illustrates the path followed, not just professionally but also personally. Each woman's mathematical contributions are explained in terms that are easily understandable by a high school or college student interested in what a mathematics career may be like. This book provides an excellent complement and companion volume to the recently reviewed Women in Mathematics: The Addition of Difference, by Claudia Henrion.

The majority of the women featured are or were academics, but some developed careers in government and industry. The tension between career and marriages, husbands, partners, children and other family responsibilities is a central part of their experience. These are real people, trying to find a balance between lives and careers just as the rest of us struggle to do. Many of the stories can serve to provide encouragement for young women contemplating a career in the mathematical sciences, and also for those who just wonder what it might be like.

The obstacles of gender and racial discrimination that some of these women faced in pursuing a mathematical career are vividly portrayed. For example, Lenore Blum was not admitted to MIT for her undergraduate work because there were only 20 dormitory beds available for women. She was married at 18 and her mother cared for her son while she worked on her thesis. More than one woman (McDuff, Kovalevsky) wrote two or more dissertations. Vivienne Malone-Mayes could not join her classmates and advisor in discussing mathematics over coffee because she was black. She was denied a teaching assistantship, also because she was black. She could not enroll in one professor's classes because he refused to teach blacks and furthermore believed that it was a waste of taxpayer's money to educate women! And in case we think we need no further vigilance, Joan Sterling Langdon, a student of Mary Gray's, was one of only three African American women who earned a Ph.D. in mathematics or mathematics education in the US in 1989.

Many of these women were married to mathematicians or scientists. There are several discussions of the two body problem of finding a position for a husband and wife pair at the same institution, and how difficult it was because of nepotism laws.

The women in academic positions clearly excelled in the three components of such a career -- teaching, research and service -- and the contributing authors provide many examples of these efforts. Many of them rose to the position of department chair and most were instrumental in developing policy for mathematics departments. Many of them were advocates for women, blacks, minorities of any kind. Unequivocally, one is left with the conviction that women have done, can do, and continue to do mathematics.

Despite their success, self-doubt seems to be a common thread running through the stories of these women. Many of them wondered whether they had what it would take to be successful, sometimes even after they had earned a Ph.D. and were holding an academic position (see, for example, Dusa McDuff). Leone Burton, a math educator, comments that as an undergraduate she didn't have even one woman teacher who might serve as a role model or as a source of encouragement. In contrast, others (see Michelson) report getting continual feedback from their professors as well as encouragement to continue on to graduate school. It is clear that these women welcomed any encouragement, however small, and whenever encouragement was received it went a very long way towards keeping them going in the face of adversity and lack of confidence. Rhonda Hughes says of her college mathematics experience: "It took so little to encourage me, but it was so important."

There is one outright error, on page 39: Émilie du Châtelet lived in the 18th, not the 17th, century. There is also a very misleading statement on page 65 about the proof of Fermat's Last Theorem. The author suggests that Andrew Wiles' proof was only possible with the use of computers. This is not the case. Wiles' proof was in fact a traditional "pencil and paper" proof, although the fact that people could check the Shimura-Taniyama conjecture computationally was an important part of the reason it came to be accepted as likely to be true.

Overall, I would recommend *Notable Women In Mathematics* to high school teachers of mathematics, high school counselors, high school students interested in mathematics, and also to college professors and students of mathematics looking for a connection to the diverse community of women mathematicians. This book is a wonderful source of role models for young women who may be attracted to mathematics but who may at the same time be repelled by the stereotypical image of the lone, slightly mad, probably male, certainly eccentric mathematician.

Libby Krussel (krussel@selway.umt.edu) is assistant professor of mathematics education in the Department of Mathematical Sciences at The University of Montana, Missoula, MT. She is interested in the preparation and professional development of mathematics teachers and teaches classes for them such as geometry, history of mathematics, algebra, modeling. She has a long-standing interest in history of mathematics and in particular the place of women in that history.