Reading this book is like a long, pleasant conversation. You can remember what you talked about, and what people said, but sometimes it is hard to figure out how you got from one topic to another. There are four tales in this conversation, bound together by the same smooth and invisible threads that make friendly discourse seem to flow so effortlessly.
Davis admits that he is "fond of listening to and telling stories," and boasts that he has been called a "tangentialist." This is a book of tangents, encounters of the "second kind." Mathematics itself constitutes the "first kind."
There is a little bit of the mathematics of the "first kind" in the first of the four sections of the book, "Napoleon's theorem." The theorem states that the centers of equilateral triangles drawn on the sides of a given triangle are the vertices of yet another equilateral triangle. The theorem is an example of some of the geometry of triangles that was not known to Euclid. As a youth, Davis came across this theorem as an exercise, and he found that he was unable to solve it. He eventually gave up, but, like a bad penny or a seasonal allergy, he kept coming across it again and again.
There are some who suspect that Napoleon's theorem is not really Napoleon's, but, perhaps LaGrange's, or someone else's. (Just as there are some who claim that William Shakespeare didn't write all those plays, but someone else who had the same name wrote them.) The second section seems to be an account of Davis futile search for the true roots of Napoleon's theorem. It only seems to be that. It is really a sketch of the New England humanist and classicist Alexander Sedgewick Carpenter, Davis' friend and sometime collaborator in the search for the genealogy of Napoleon's theorem.
The third and shortest section of the book describes Davis' graduate education, his relationship with his advisor, Stefan Bergman, the crush Davis had on movie star Liesel Bergner, and how both Bergman and Bergner endured the loneliness of exile from their homelands.
Davis repeats a story about Bergman and his wife, Dr. Hilda Geiringer, and how they missed the European ways with which they had grown up. Davis quotes Clifford Truesdell:
"In later years Hilda Geiringer told my wife and me a story about Bergman. When all America had come to call everybody Bill and Jane, he asked her if he could speak to her alone in complete secrecy. She agreed. He said: I know that now in public we have to be Hilda and Stefan, but when we are alone together, may I still call you Frau Dr. Geiringer and will you call me Herr Dr. Bergman?"
The last and longest section, "The Rothschild I Knew," is an account of Davis' friendship with Lord Victor Rothschild. The friendship began in January, 1986, when Rothschild sent Davis a note about a small error he had found in one of Davis' books, and it ended with Rothschild's death in March, 1990. In just four years, they managed to become old friends.
The book concludes with some notes about the number theory that provided some of the fuel for their friendship. Thus, the book closes a number of circles, from Euclid as a geometer to Euclid as a number theorist, from Napoleon to Rothschild as amateur mathematicians, from Davis New England friend Alexander Sedgwick Carpenter to his English friend Lord Victor Rothschild.
"Mathematical Encounters of the 2nd Kind" is a very pleasant book, an appealing tale of the life and friends of a mathematician. It is well worth the time it takes to read it.
Publication Data:
Mathematical Encounters of the 2nd Kind, Philip J. Davis, Birkhauser, 1997. 304 pages, ISBN 0-8176-3939-X
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Ed Sandifer ( sandifer@wcsu.ctstateu.edu) is a professor of mathematics at Western Connecticut State University and an enthusiastic fan of Leonhard Euler.
Read This! is the MAA Online book and software review column. Contributions are welcome; contact the editor if you'd like to be one of our reviewers. Books for review should be sent to the editor: Fernando Gouvêa, Dept. of Math&CS, Colby College, Waterville, ME 04901.