Remarkable Mathematicians From Euler to von Neumann, Ioan James, Cambridge University Press, 2002, 320 pp, paper, ISBN 0521520940, $28.95, distributed by The Mathematical Association of America, P.O. Box 91112, Washington, D.C. 20090-1112. MAA catalog code RMA/YD03. 1-800-331-1622 or www.maa.org .
Remarkable Mathematicians is a collection of 60 biographies grouped chronologically by birth year into sets of six commencing with Euler in 1707 and terminating with Von Neumann in 1903. The author's stated intention is to “convey in human terms something of the way in which mathematics developed.” There is a strong emphasis on the role of mentors and the progress of mathematics education in general. There is discussion of important social issues such as anti-Semitism and the subsequent emigrations to America. A strong point of the work is that wherever possible the author motivates each biography using quotes from contemporaries. While these quotes are identified by source in an appendix at the back of the work, page numbers are not given. A major problem is the lack of an index. One becomes particularly aware of this when trying to find references to names that seem to be missing from the development.
Collected biographies of mathematicians can vary in depth from E.T. Bell's Men Of Mathematics to the Dictionary of Scientific Biography. Remarkable Mathematicians seems to be closer in spirit to the former while avoiding much of the hyperbole that Bell is known for. However, there is less detail given to the development of the actual mathematics. In creating a roster of candidates for inclusion in such a work, one is faced with the daunting task of representing the whole of post-classical mathematics. If one compares the 60 biographies contained in Remarkable Mathematicians to Bell's work, 22 had been previously developed, 10 are expansions of shorter references, 15 expand single references but only 13 completely new biographies are introduced. There are only three female and two non-western biographies included. Mathematicians who are referred to frequently such as Hurwitz, Jordan, and Lebesgue did not receive their own biography. The debate on foundations between Hilbert and Brouwer makes no reference to the work of Frege, Russell, and Whitehead. Noticeably missing are Lobachevsky and Bolyai so that non-Euclidean geometry is given only a cursory treatment. Other notable absentees include Bolzano, Lambert, Moebius, Venn, Peano, Markov, and Zermelo. The author champions Henry Smith, yet only refers to George Boole in passing. By concluding in 1903 the opportunity of including Goedel and Turing is missed. I believe that this is a useful book, but it would have been more satisfying had the author begun later in the XVIII century and included more biographies that still need to be passed on.
Jim Kiernan, Adjunct Professor, Brooklyn College