## The Housekeeper and the Professor

Some time ago, I heard about a book from Japan called The Housekeeper and the Professor, written by Yoko Ogawa in 2003 and translated by Stephen Snyder last year. As the title suggests, the book centers on the relationship between a housekeeper, her son, and a math professor. The main conceit of the book is that the Professor suffered an accident some years before that impaired his memory, so that his short term memory only lasts around 80 minutes. In other words, every day the housekeeper and her son come to visit the professor, it is as if they are meeting him for the first time. He copes by clipping small notes to his clothing, and in spite of his disability he still dabbles in mathematics.

One part Memento, one part A Beautiful Mind, the book was named a New York Times Book Review Editors' Choice, and was popular enough in Japan to warrant a film adaptation (the Japanese language trailer for which can be found below). Clearly, then, the book has resonated with people regardless of language. But how does the book stack up from a mathematical perspective?

At first glance, it may sound like there's a lot of fodder for me to complain about here. After all, how many times have we seen mathematicians in popular culture with some sort of mental handicap? Granted, memory loss is a new twist - usually insanity is the preferred condition. Still, though, I don't think it's too much to ask for a mathematician who's just a normal dude (or even, gasp, a normal lady).

Unfortunately, he is also but the latest entry in a long line of mathematicians in popular culture who are socially maladjusted. He's also incredibly reclusive - he has a strong aversion to crowds, and when he accompanies the housekeeper and her son to a baseball game midway through the novel, it's fairly clear that he hasn't been on an outing in some time. One could explain these traits as a byproduct of his mental condition, of course: it's natural for him to be shy around people when he is always meeting them for the first time, and there's a danger in taking him out for too long lest he should forget what he's doing out in the first place. But part of me feels like these are convenient excuses for rehashing familiar tropes about people who study mathematics.

It's not all bad, though. In fact, I found myself able to forgive much of what I didn't like about this portrayal of mathematicians, because there are many positive features about the professor as well. For starters, the professor is able to form a close relationship to the housekeeper's son (who he nicknames Root, because the child's flat head of hear reminds him of the square root sign). Even though the professor can't remember who Root is from day to day, every time the boy comes to the professor's house, the professor dotes on him like a father. He obsesses over the safety of Root more than the housekeeper, and keeps Root in his mind as much as he can, given his circumstances.

Of course, his concern about Root wouldn't be complete if it didn't include concern over his mathematics education. Here's another thing Ogawa does quite well - she is able to not only show the professor's love of mathematics, but she is also able to illustrate how that passion can inspire others. The professor is a number theorist, and he is always looking for meaning behind numbers (something which, in the hands of a poorer story-teller, would no doubt incite my rage). What makes the professor's interest significant is that he never discusses numbers for the sake of random numerological connections - instead, he is able to take small observations and use them to hint at larger mathematical ideas. Here's one such example, from the day the three of them went to a baseball game (this may be my favorite passage from the book):

And when he noticed that his seat number was 714 and Root's was 715, he began to lecture again and completely forgot to sit down.

"The home run record Babe Ruth set in 1935 is 714. On April 8, 1974, Hank Aaron broke that record, 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: 714 × 715 = 2 × 3 × 5 × 7 × 11 × 13 × 17 = 510510. And, the sum of the prime factors of 714 equals the sum of the prime factors of 715: 714 = 2 × 3 × 7 × 17, 715 = 5 × 11 × 13; 2 + 3 + 7 + 17 = 5 + 11 + 13 = 29. A pair of consecutive whole numbers with these properties is quite rare. There are only 26 such pairs up to 20,000. This one is the Ruth-Aaron pair. Just like prime numbers, they are more rare as the numbers get larger. And 5 and 6 are the smallest pair. But the proof to show that those pairs are infinite in number is quite difficult*. . . . The important thing is that I'm sitting in 714 and you're in 715, instead of the opposite. It's the young who have to break the old records. That's the way the world works, don't you think?" (90)

Happy to have broken the home run record, or happy to be part of an interesting number phenomenon?

There are vignettes like this peppered throughout the book, where the professor will link an everyday observation to some kind of mathematics. In the story, which is told from the housekeeper's perspective, we see how this inspires the housekeeper to think about simple mathematical problems. In spite of her lack of formal training, the professor is able to inspire in her a sense of mathematical curiosity (something which all math teachers should aspire to do). Those of the mathematical persuasion are rarely shown as being able to interest people who are less mathematically inclined. I'm glad to see that this book bucks that trend.

Moreover, this book does a better than average job of discussing what makes mathematics so appealing to those of us who study it. Consider the following exchange between the housekeeper and the professor, after she apologizes for sending a proof of his to a journal via regular mail instead of express:

"No, there was no need to send it express. Of course, it's important to arrive at the correct answer before anyone else, but it's just as important that the proof is elegant."

"I had no idea a proof could be beautiful . . . or ugly."

"Of course it can," he said. Getting up from the table, he came over to the sink where I was washing the dishes and peered at me as he continued. "The truly correct proof is one that strikes a harmonious balance between strength and flexibility. There are plenty of proofs that are technically correct but are messy and inelegant or counterintuitive. But it's not something you can put into words---explaining why a formula is beautiful is like trying to explain why the stars are beautiful." (16)

While I don't necessarily agree with the last part, I think it's refreshing to find a discussion of what accounts for mathematical beauty in a book like this. This type of discussion between a mathematical expert and a mathematical amateur is not often present in works that center on mathematics - more frequently, the conversation is between math experts, or is not about mathematics at all. Providing this type of simple insight to a reader who may not have a mathematical background is certainly a plus.

Despite falling into some tired stereotypes, the professor emerges as a fully realized character. His memory problems are much more than a gimmick, and while they enable certain stereotypes to persist, Ogawa also uses his disability to showcase a degree of empathy for other people that is not often found in portrayals of those who study mathematics. Overall I found that I quite enjoyed the book - if you've got a lazy Sunday coming up (the book is short, so you could easily finish it in a weekend), I'd certainly recommend giving this story a shot.

*Actually, the question as to whether or not there are infinitely many such pairs is actually still open. See here for more information.

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