Yôko Ogawa - The Gift of Numbers aka The Housekeeper and the Professor

We prayed longer that day for the fawn than we did for my mother's soul. We prayed that the tiny life could go with her on her journey.

The next day, I found a picture of Root's father in the local paper. It seemed he had won a research prize given by some foundation. It was just a short article with a blurry picture of a man ten years older than when I had known him, but there was no doubt it was him.

I closed the paper, crumpled it into a ball, and threw it in the garbage. Then, thinking better of it, I fished it out, smoothed the wrinkles, and cut out the article. It looked like a little piece of trash.

"What's the big deal?" I asked myself. "No big deal at all," I replied. "Root's father won a prize. Happy day. That's it."

I folded the article and put it away in the box that held the stump of Root's umbilical cord.

I thought of the Professor whenever I saw a prime number-which, as it turned out, was almost everywhere I looked: price tags at the supermarket, house numbers above doors, on bus schedules or the expiration date on a package of ham, Root's score on a test. On the face of it, these numbers faithfully played their official roles, but in secret they were primes and I knew that was what gave them their true meaning.

Of course, I couldn't always tell immediately whether a number was prime. Thanks to the Professor, I knew the prime numbers up to 100 just by their feel; but when I encountered a larger number that I suspected might be prime, I had to divide it to be sure. There were plenty of cases where a number that looked to be composite turned out to be prime, and just as many others where I discovered divisors for a number that I was certain was prime.

Taking my cue from the Professor, I started carrying a pencil and a notepad around in the pocket of my apron. That way, I could do my calculations whenever the mood struck. One day while I was cleaning in the kitchen in the tax consultants' house, I found a serial number engraved on the back of the refrigerator door: 2311. It looked intriguing, so I took out my notepad, moved aside the detergent and the rags, and set to work. I tried 3, then 7, and then 11. All to no avail. They all left a remainder of 1. Next I tried 13, and 17, and 19, but none of them was a divisor. There was no way to break up 2,311; but, more than that, its indivisibility was positively devious. Every time I thought I had spotted a divisor, the number seemed to slip away, leaving me oddly exhausted yet all the more eager for the hunt-which was always the way with primes.

Once I'd proved that 2,311 was prime, I put the notepad back in my pocket and went back to my cleaning, though now with a new affection for this refrigerator, which had a prime serial number. It suddenly seemed so noble, divisible by only one and itself.

I encountered 341 while I was scrubbing the floor in their office. A blue tax document, Form 341, had fallen under the desk.

My mop stopped in midstroke. It had to be prime. The form was covered with dust from sitting under the desk for so long, but 341 called out to me; it had all the qualities that would have made it a favorite of the Professor.

My employers had gone home and so I set about checking the number in the darkened office. I hadn't really developed a system for finding divisors, and I ended up relying mostly on intuition. The Professor had shown me a method invented by someone named Eratosthenes, who had been the librarian at Alexandria in ancient Egypt, but it was complicated and I'd forgotten how to do it. Since the Professor had such great respect for intuition when it came to numbers, I suspected he would have been tolerant of my method.

In the end, 341 was not a prime: 341 ÷ 11 = 31. A wonderful equation, nonetheless.

Of course, it felt good when a number turned out to be prime. But I wasn't disappointed if it did not. Even when my suspicions proved unfounded, there were still things to be learned. The fact that multiplying two primes such as 11 and 31 yielded a pseudo-prime such as 341, led me in an unexpected direction: I now found myself wondering whether there might be a systematic way to find these pseudo-primes, which so closely resembled true prime numbers.

But despite my curiosity, I set the form on the desk and rinsed my mop in the murky bucket. Nothing would have changed if I'd found a prime number, nor if I'd proven that one wasn't prime. I was still facing a mountain of work. The refrigerator went on keeping things cold, regardless of its serial number, and the person who had filled out Form 341 was still struggling with his tax problems. The numbers didn't make things better; perhaps they even made them worse. Perhaps the ice cream was melting in that refrigerator, I certainly wasn't making any progress mopping the floor, and I suspected my employers would be unhappy with my work. But for all that, there was no denying that 2,311 was prime, and 341 was not.

I remembered something the Professor had said: "The mathematical order is beautiful precisely because it has no effect on the real world. Life isn't going to be easier, nor is anyone going to make a fortune, just because they know something about prime numbers. Of course, lots of mathematical discoveries have practical applications, no matter how esoteric they may seem. Research on ellipses made it possible to determine the orbits of the planets, and Einstein used non-Euclidean geometry to describe the form of the universe. Even prime numbers were used during the war to create codes-to cite a regrettable example. But those things aren't the goal of mathematics. The only goal is to discover the truth." The Professor always said the word truth in the same tone as the word mathematics .

"Try making a straight line right here," he'd said to me one evening at the dinner table. Using a chopstick for a ruler, I traced a line on the back of an advertising leaflet-our usual source of scrap paper. "That's right. You know the definition of a straight line. But think about it for a minute: the line you drew has a beginning and an end. So it's actually a line 'segment'-the shortest distance connecting two points. A true line has no ends; it extends infinitely in either direction. But of course, a sheet of paper has limits, as do your time and energy, so we use this segment provisionally to represent the real thing. Now furthermore, no matter how carefully you sharpen your pencil, the lead will always have a thickness, so the line you draw with it will have a certain width, it will have a surface area, and that means it will have two dimensions. A real line has only one dimension, and that means it is impossible to draw it on a piece of real paper."

I studied the point of the pencil.

"So you might wonder where you would ever find a real line-and the answer would be, only in here." Again, he pointed at his chest, just as he had when he had taught us about imaginary numbers. "Eternal truths are ultimately invisible, and you won't find them in material things or natural phenomena, or even in human emotions. Mathematics, however, can illuminate them, can give them expression-in fact, nothing can prevent it from doing so."

As I mopped the office floor, my mind churning with worries about Root, I realized how much I needed this eternal truth that the Professor had described. I needed the sense that this invisible world was somehow propping up the visible one, that this one, true line extended infinitely, without width or area, confidently piercing through the shadows. Somehow, this line would help me find peace.

I had just got back from shopping and was about to start dinner for the tax consultants when a call came from the secretary at the Akebono Housekeeping Agency.

"Get right over to that mathematician's house. It seems your son has done something to upset them. I don't know what happened, but get over there now. That's an order from the Director."