Read This!

The MAA Online book review column

Briefly Noted

Short Reviews by Fernando Q. Gouvêa

August 1999

A new edition of Dirichlet's Lectures on Number Theory would be big news any day, but it's particularly gratifying to see the book appear as "the first of an informal sequence" which is to include "classical mathematical works that served as cornerstones for modern mathematical thought." Editions and translations of such works have been in short supply, and those of us who are interested in the history of mathematics can often be heard to lament that this or that crucial source is no longer available. So all power to the American Mathematical Society and the London Mathematical Society in their joint-venture History of Mathematics series: may the "Sources" subseries live long and prosper.

What about the current book? Dirichlet's Lectures was the first real textbook in number theory, intended for (advanced) students rather than for researchers in the area. In contrast to Gauss's famously difficult Disquisitiones Arithmeticae, this is quite accessible, and could almost be used as a textbook still today. In addition to Dirichlet's lectures, the book includes several supplements by Richard Dedekind which complement the text in various ways. The two final supplements, which were the beginning of algebraic number theory, were not included here, mostly because Cambridge University Press has recently published a translation of Dedekind's Theory of Algebraic Integers (see our earlier note). I rather regret this, since I'd have enjoyed reading those famous first steps, but the regret is swallowed up by my delight in having the Dirichlet text available. For those who like to heed Abel's admonition to "read the masters, not their students," here's a great opportunity to learn more about Number Theory.

When a book that has a mathematician as one of its main characters manages to hit the New York Times bestseller list, mathematicians should pay attention. Neal Stephenson's Cryptonomicon is a complex and multilayered novel, somewhat reminiscent of Thomas Pynchon's Gravity's Rainbow. Much of the story turns around cryptography, both historical (during World War II) and current. The novel weaves together three narratives, two set during World War II and one set in the near future. The first narrative centers on Lawrence Pritchard Waterhouse, a brilliant "intuitive mathematician" who is always a little "out of it" when it comes to the world in general but has a natural feel for things mathematical and cryptographical. After a difficult start, Waterhouse's talents are discovered and he comes to play a crucial role in the war effort. In particular, he is assigned the task of using a kind of mathematical information theory to find a way to use the data gathered by decoding German and Japanese encrypted messages without giving away the fact that their encryption methods have been broken. The second narrative is about Bobby Shafton, a Marine who leads a secret detachment whose job it is to put into effect Waterhouse's ideas. Finally, the third narrative is about Randy Waterhouse, Lawrence's grandson, who is part of a group attempting to establish a "data haven" in an obscure part of Southeast Asia. As one might expect the stories intertwine, come into contact, and comment on each other.

At several points in the book there are comments about mathematicians and what they are like. There are many comments about how strange mathematicians are (particularly in a weird passage in which Randy has to help distribute his grandmother's things among her descendants), but at the same time the book shows great respect and admiration for mathematical talent. By making Waterhouse an intuitive genius, Stephenson sidesteps the difficult problem of portraying how a mathematician thinks, but there are occasional attempts at giving the reader a sense of Waterhouse's internal world. For example, here, at age twelve, he is contemplating the pipes of an organ:

The tops of the pipes defined a graph: not a straight line but an upward-tending curve. The organist/math teacher sat down with a few loose pipes, a pencil, and paper, and helped Lawrence figure out why. When Lawrence understood, it was as if the math teacher had suddenly played the good part of Bach's Fantasia and Fugue in G Minor on a pipe organ the size of the Spiral Nebula in Andromeda--the part where Uncle Johann dissects the architecture of the Universe in one merciless descending ever-mutating chord, as if his foot is thrusting through skidding layers of garbage until it finally strikes bedrock. In particular, the final steps of the organist's explanation were like a falcon's dive through layer after layer of pretense and illusion, thrilling or sickening or confusing, depending on what you were. The heavens were riven open. Lawrence glimpsed choirs of angels ranking off into geometrical infinity. (p. 7)

Cryptonomicon is definitely worth reading (despite its length), even though at the end the storyline seems to run out of steam a bit, and the final page isn't as satisfying as one might have anticipated. (Stephenson's earlier The Diamond Age, also a brilliant book, has the same flaw.) Overall, this may be one of the more sympathetic portrayals of a mathematician in popular literature, and though it perpetuates some of the usual stereotypes it also has much that is interesting in it. Check it out!

Publication Data

Barry Cipra, What's Happening in the Mathematical Sciences, 1998-1999. American Mathematical Society, 1999. Softcover, 126 pages, ISBN 0-8218-0766-8.

P. G. L. Dirichlet Lectures in Number Theory, with supplements by Richard Dedekind (History of Mathematics, Volume 16). American Mathematical Society and London Mathematical Society, 1999. Softcover, 275 pages, $49.00 ($39.00 to AMS members). ISBN 0-8218-2017-6.

Neal Stephenson, Cryptonomicon. Avon Books, May 1999. Hardcover, 918 pages, $27.50. ISBN 0-380-97346-4

Back Issues:

• April 1999: Reprints of "classics", books on applied mathematics.
• May 1999: Books on math and physics, both popular and technical.
• July 1999: Various kinds of geometry, and classics in applied mathematics.

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Read This! is the MAA Online book 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. Publishers, please check our reviews information page.