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

"How much did you weigh at birth?" This question was new to me.

"I was 3,217 grams," I said. Having no idea what my own weight had been, I used Root's.

"Two to the 3,217th minus 1 is a Mersenne prime," he mumbled before disappearing into his study.

During the previous month, the Tigers had managed to climb back into the pennant race. After Yufune's no-hitter, the strength of the pitching staff had given a boost to the offense as well. But at the end of June things started to unravel. They had lost six straight, and the Giants had managed to pass them, bumping the Tigers down to third place.

The housekeeper who had pinch-hit for me had been methodical, and while I had been afraid to disturb the Professor's work and had barely touched the books in his study, she had picked them all up and stuffed them into the bookshelves, stacking any that didn't fit in the spaces above the armoire and under the sofa. Apparently she had a single organizing principle: size. In the wake of her efforts, there was no denying that the room looked neater, but the hidden order behind the years of chaos had been completely destroyed.

I suddenly remembered the cookie tin filled with baseball cards and went to look for it, fearing it had been lost. It was not far from where I'd left it, now being used as a bookend. The cards inside were safe and sound.

But whether the Tigers rose or fell in the rankings, whether or not his study was neat, the Professor remained the same. Within two days, the interim housekeeper's efforts had vanished and the study had returned to its familiar state of disarray.

I still had the note the Professor had written the day of my confrontation with his sister-in-law. She hadn't seen me take it; I'd slipped it safely away into my wallet next to a photograph of Root.

I went to the library to find out about the formula. The Professor would certainly have explained it to me if I'd asked, but I felt that I would have a much deeper understanding if I struggled with it alone for a while. This was only a feeling, but I realized that during my short acquaintance with the Professor I had begun to approach numbers in the same intuitive way I'd learned music or reading. And my feelings told me that this short formula was not to be taken lightly.

The last time I'd been to the library was to borrow books on dinosaurs for a project Root had been assigned during his school vacation last summer. The mathematics section, at the very back of the second floor, was silent and empty.

In contrast to the Professor's books, which showed signs of their frequent use-musty jackets, creased pages, crumbs in the binding-the library books were so neat and clean, they were almost off-putting. I could tell that some of them would sit here forever without anyone cracking their spines.

I took the Professor's note from my wallet.

e π i+ 1 0

His handwriting was unmistakable: the rounded forms, the wavering lines. There was nothing crude or hurried about it; you could sense the care he had taken with the signs and the neatly closed circle of the zero. Written in tiny symbols, the formula appeared almost modest, sitting alone in the middle of the page.

As I studied it more closely, the Professor's formula struck me as rather strange. Although I could only compare it to a few similar formulas-the area of a rectangle is equal to its length times its width, or the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides-this one seemed oddly unbalanced. There were only two numbers-1 and 0-and one operation-addition. While the equation itself was clear enough, the first element seemed too elaborate.

I had no idea where to begin researching this apparently simple equation. I picked up the nearest books and began leafing through them at random. All I knew for sure was that they were math books. As I looked at them, their contents seemed beyond the comprehension of human beings. The pages and pages of complex, impenetrable calculations might have contained the secrets of the universe, copied out of God's notebook.

In my imagination, I saw the creator of the universe sitting in some distant corner of the sky, weaving a pattern of delicate lace so fine that even the faintest light would shine through it. The lace stretches out infinitely in every direction, billowing gently in the cosmic breeze. You want desperately to touch it, hold it up to the light, rub it against your cheek. And all we ask is to be able to re-create the pattern, weave it again with numbers, somehow, in our own language; to make even the tiniest fragment our own, to bring it back to earth.

I came across a book about Fermat's Last Theorem. As it was a history of the problem, not a mathematical study, I found it easier to follow. I already knew that the theorem had remained unsolved for centuries, but I had never seen it written down:

"For all natural numbers greater than 3, there exist no integers x, y, and z, such that: x n+ y n= z n.

Was this all there was to it? At first glance it seemed that any number of solutions could be found. If n = 2, you get the wonderful Pythagorean theorem; did that mean that by simply adding 1 to n , the order was irrevocably lost? As I flipped through the book, I learned that the proposition had never been published in a formal thesis but was something Fermat had scribbled in the margins of another document; apparently he had not left a proof, having run out of space on the page. Since then, many geniuses have tried their hand at solving this most perfect of mathematical puzzles, all to no avail. It seemed sad that one man's whim had been bedeviling mathematicians for more than three centuries.

I was impressed by the delicate weaving of the numbers. No matter how carefully you unraveled a thread, a single moment of inattention could leave you stranded, with no clue what to do next. In all his years of study, the Professor had managed to glimpse several pieces of the lace. I could only hope that some part of him remembered the exquisite pattern.

The third chapter explained that Fermat's Last Theorem was not simply a puzzle designed to excite the curiosity of math fanatics, it had also profoundly affected the very foundations of number theory. And it was here that I found a mention of the Professor's formula. Just as I was aimlessly flipping through pages, a single line flashed in front of me. I held the note up to the page and carefully compared the two. There was no mistake: the equation was Euler's formula.

So now I knew what it was called, but there remained the much more difficult task of trying to understand what it meant. I stood between the bookshelves and I read the same pages several times. When I was confused or flustered, I did as the Professor had suggested and read the lines out loud. Fortunately, I was still the only person in the mathematics section, so no one could complain.

I knew what was meant by π. It was a mathematical constant- the ratio of a circle's circumference to its diameter. The Professor had also taught me the meaning of i. It stood for the imaginary number that results from taking the square root of -1. The problem was e. I gathered that, like π, it was a nonrepeating irrational number and one of the most important constants in mathematics.

Logarithm was another term that seemed to be important. I learned that the logarithm of a given number is the power by which you need to raise a fixed number, called the base, in order to produce the given number. So, for example, if the fixed number, or base, is 10, the logarithm of 100 is 2: 100 = 10 2or log 10100.

The decimal system uses measurements whose units are powers of ten. Ten is actually known as the "common logarithm." But logarithms in base e also play an extremely important role, I discovered. These are known as "natural logarithms." At what power of e do you get a given number?-that was what you called an "index." In other words, e is the "base of the natural logarithm." According to Euler's calculations: e = 2.71828182845904523536028… and so on forever. The calculation itself, compared to the difficulty of the explanation, was quite simple: