The Mathematical Career of Pierre de Fermat, 1601-1665 (review)

Abstract

REVIEWS 371 Especially fascinating is this book's analysis of atypical photographs of famous women—a risque Eleanor Roosevelt, a familial Gertrude Stein dandling her nephew on her knee, a flight-suited Anne Morrow Lindbergh as copilot for her husband. Wagner-Martin shows how these photographs revise the usual restrictive images of these women, stock images that reinforce the cliches and preconceptions that hobble biographers as they approach a subject. One of the objectives in studying women of the past—and present—is to discover inspiring precursors. Yet a new biographical pitfall has supplanted the hagiographie maternal and wifely platitudes of the past, the temptation to see all women's lives as feminist narratives, to find in every female biography a paradigm of feminist achievement. As feminist biographers, critics, and historians, we naturally want to locate a perfect map, a feminist profile of personal discovery and affirmation wherever we can find it, but we must also avoid taking Procrustean steps to deliver this model, rather than face the unwelcome news that not every famous woman has the feminist commitments we might wish to discover. Indeed, the stories of women who turned coat, who opposed feminist initiatives, who neglected other women, who want to remain the only woman in the boardroom , have lessons to teach us as well, albeit harsh ones. Reading biography is one way of reminding us of the long road to reform. Annette Wheeler Cafarelli Columbia University MICHAEL SEAN MAHONEY, The Mathematical Career of Pierre de Fermât, 16011665 . 2d edition. Princeton: Princeton UP, 1994. xx + 432 pp. |18.95 paperback . A complete biography of Fermât would include details of his personal and professional life, along with his mathematical career. This book focuses on the latter aspect, yet so much is included of his background and administrative career that one must regard this work as definitive. Mahoney is Professor of History at Princeton. The first edition (1973) represented five years of work at the beginning of his career. This edition incorporates corrections, results from more modern literature, and his own research in later years. A modern academic, reading Mahoney's biography of Fermât, would be struck by the thin network of numerical practitioners in the seventeenth century, and the lack of publication outlets. Indeed, our modern apparatus of scholarly communication had not yet been invented, or was in its raw infancy. This sets in perspective the intriguing task faced by Mahoney: how to show the brilliance of Fermat's thinking, the rather quick pace of dissemination of Fermat's results in the face of his reluctance to publish, and the necessity of inventing equations that would make Greek and Arab discoveries and conjectures usable by his correspondents. Fermât is best known by today's layman for his "Last Theorem," written in the margin of a book, saying that he did not have enough room to show a truly marvelous demonstration that what any schoolboy knows as the Pythagorean theorem on right triangles, x2 + y2 = z2, had no solution except when the exponent was 2. Apart from that statement, Fermât created modern number theory (it was 372 biography Vol. 18, No. 4 ignored for many decades), was one of the inventors of analytic geometry, and unknowingly laid early foundations for differential and integral calculus. But Mahoney quite clearly states: "Fermât sought neither curves nor functions; he sought areas, and he found them. . . . He did not invent the calculus." Along with Pascal, he created certain theoretical guidelines for probability theory—and all this while being a shy and reclusive bureaucrat in Toulouse. Born at the beginning of the century, Fermât enjoyed the advantage of wealth. He attended the university at Toulouse, graduated in law, and purchased the offices of conseiller and commissaire with the help of his wife's dowry. He was then able to add de to his name as a member of the noblesse de robe. One of his rare noted professional deeds was to help "organize the customary laws of his birthplace , Beaumont." Mahoney first sketches the diversity of numerical efforts in the seventeenth century, in six categories: the classical geometers, to whom the young Fermât was sympathetic; the cossist...