## The Beauties of Mathematics Explained

September 21, 2009

Book Review
Philip J. Davis

The Housekeeper and the Professor. By Yoko Ogawa, translated by Stephen Snyder, Picador, New York, 2009, Soft Cover, 192 pages, \$14.00.

Yoko Ogawa is a prolific, prize-winning writer whose productions in a variety of subjects, genres, and media have been frequently translated from the Japanese. For The Housekeeper and the Professor, she drew on her collaboration with mathematician Masahiko Fujiwara. A movie based on the book was released in Japan in 2006.

I will say at the outset that it is probably unfair to the author to have her book reviewed by a professional mathematician. A poet with only a grade-school knowledge of mathematics might have been a more appropriate choice. But here goes.

The story, told by the unnamed housekeeper, is simple enough. The mind of the (also unnamed) professor of mathematics, for whom the housekeeper works, has degenerated; at any given time, he is able to recall only the preceding eighty minutes. As part of his mental condition, he is obsessed by numbers and repeats number-related questions---such as "What's your shoe size?"---over and over.

Hearing a number, the professor immediately perceives some mathematical fact or relationship and is impelled to divulge it.

"Your birthday is February 20th. 2 20. Can I show you something?"

The professor takes off his wristwatch, a prize that he won before the onset of his mental condition, and shows it to the housekeeper. On its back is engraved "President's Prize No. 284." In this way, the author introduces the reader to the "amicable pair" 220 and 284, in which the divisors of the first add up to the second, and vice versa.

In his mania, or perhaps because of it, the professor is able to convey to his housekeeper and to her young son the beauty, the surprises, and the variety of features that numbers have as they occur in the elementary theory of numbers. We read about factorials, factorization, primes, twin primes, triangular numbers, perfect numbers, and so forth. Stuck in, like a plum in a plum pudding, is an assertion that serves to inform us of the professor's professional credentials from the time when he still had his mathematical marbles: He "worked on Artin's conjecture about cubic forms with whole-number coefficients."

Japanese baseball teams and their history constitute a submotif that is woven throughout this short novel. That baseball is very likely the most mathematized, the most statisticized of all the sports provides the author with numerous opportunities to link the sport with the professor's obsession. The reader may be amused, amazed, excited, or simply bored by the following instance of numerological baseball cited by the professor:

"The home run record of Babe Ruth is 714. On April 8, 1974, Hank Aaron broke that record by hitting his 715th off of Al Downing of the Dodgers. The product of 714 and 715 is equal to the product of the first seven prime numbers: 714x715 = 2x3x5x7x11x13x17 = 510510. And the sum of the prime factors of 714 equals the sum of the prime factors of 715 . . . ."

Yes, Elizabeth, there really are people---laymen, amateurs, even professionals---who specialize in sniffing out such ingenious connections. And yes, there are people who find hidden meaning, cosmic or religious, in such fortuitous coincidences. The universe, they say, is trying to tell us something this way, if only that mathematics is the magic basis of everything. I once heard a puritan defined as a person who worries that someone, somewhere is enjoying himself. I am no puritan, and if someone finds pleasure in this sort of thing, why should I deny her that pleasure?

Ogawa's story is simply and delicately told and has a didactic aspect. It is that anyone---even a (female!) housekeeper---can come to appreciate and enjoy mathematics. It is quite possible that a young person, reading Ogawa's book, will be drawn into a wider knowledge of mathematics than is inculcated by standard curricula, or even into deep mathematical professionalism.

Yet I am bothered by this book, largely because it bolsters certain popular stereotypes (occasionally true, alas) of mathematicians and their activity. Thus, mathematicians are obsessive nuts, and what they like to do is far removed from anything sensible or practical. They take joy in finding larger and larger primes or amicable pairs or in looking around and finding such coincidences as the Babe Ruth�Hank Aaron connection. The reader also learns that what mathematicians do, beyond the very simple, cannot be easily explained to the general public (e.g., Artin's conjecture). Finally, the author implies that the principal virtue of mathematics lies in its aesthetic qualities, qualities that, in my experience, are loudly trumpeted but not easily grasped.

Someone once wrote that mathematics is celestial poetry, a view that is promoted here. I seek a more earthbound interpretation.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at [email protected].

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