Find X.(Unknown Quantity: A Real and Imaginary History of Algebra)(Book review)

Unknown Quantity: A Real and Imaginary History of Algebra, by John Derbyshire (Joseph Henry, 390 pp., $27.95)

IN 1935, a prominent man eulogized one of his friends: "There is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual's own feeling, thinking, and acting. The genuine artists, investigators, and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, nonetheless the fruits of their endeavors are the most valuable contributions which one generation can make to its successors."

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If you have not yet read John Derbyshire's delightful and challenging history of algebra, Unknown Quantity, you might well think that this passage was written by one artist, about another. In a sense it was: The author was Albert Einstein, and he was writing about Emmy Noether, who ranks among the most accomplished mathematicians. One of her greatest accomplishments was to discover a connection between certain mathematical structures and symmetries in physics.

With this new book, Derbyshire establishes himself as one of our foremost expositors of mathematics. His previous effort in this area, Prime Obsession, was a gem; Unknown Quantity is a 100-carat necklace. While Prime Obsession focused on the Riemann Hypothesis, a single problem that has animated mathematicians for almost a century and a half, Unknown Quantity presents the entire two-millennia-long epic of algebra.

Popular culture--in such films as Proof, Pi, and A Beautiful Mind--tends to portray creative mathematicians as exceedingly odd, even warped individuals. Derbyshire is closer to the truth in telling how ordinary are the lives of most mathematicians. He does note the occasional oddity: Galois's fatally reckless romanticism, Grothendieck's mystic environmentalism. But the drama of this history lies not in the struggles or eccentricities of the people but in the mathematics itself.

Derbyshire both understands and respects the lay reader of mathematics. He knows that the typical reader will be unfamiliar with advanced mathematics, but he also respects that reader's ability to learn something about it. Such an attitude requires courage on the part not only of the author but of the publisher as well. Most publishers will not touch a popular book with an equation or two in it; Joseph Henry Press is to be applauded.