The Mathematician' s Brain, David Ruelle, 2007, 160pp. $22.95 cloth, ISBN 0691129827, Princeton University Press, Princeton, NJ. www.press.princeton.edu
Readers of The Mathematician's Brain will be immediately charmed by the eloquence of the narrative. With a touch of humor and obvious respect for his peers, Ruelle's very human presentation of the mathematically inclined will keep the reader interested.
Ruelle delves into an in-depth examination of Felix Klein's astute observation that there are different geometries and problem solving becomes easier if problems can be categorized appropriately. The clarity of this and other mathematical explanations in The Mathematician's Brain highlight how mathematicians achieve: an often solitary enterprise comprised of part innate ability and part curiosity mixed with a need to generalize and very often with a touch of cleverness.
Ruelle's interest in the formal structures of modern day mathematics appears in several chapters. He notes that we have moved significantly from the august work of the ancient Greeks to a formalized system in which even the work of the earliest mathematicians may be derived. He makes the argument that the modern system gives the research mathematician an important set of tools, but it does not replace the conceptual understanding and mathematical intuition needed to further mathematics as a science.
Lastly, Ruelle's presentation of his appreciation for the work of and his empathy for the personal struggles of both his colleagues and his predecessors really illustrates the sometimes hidden humanity of mathematicians, making The Mathematician's Brain a pleasure to read.
If you are looking for a journey through a wonderfully multifaceted exposition of what it means to think mathematically, peruse The Mathematician's Brain.
Kathleen Ambruso Acker, Ph.D.