The Gift of Numbers (13 page)

Not long after that, I received a message from the agency asking
me to report for work again at the Professor's house. I could not
say whether the widow had a change of heart, or had simply never
liked the new housekeeper. I also had no way of determining
whether the absurd misunderstanding had been settled or not.
But the Professor had now earned his eleventh star.

No matter how many times I went over the strange scene in my
mind, it remained a mystery. Why did the widow report me to the
agency and have me fired? Why had she reacted so strongly to
Root's visit? I was sure she had spied on us from the garden that
night after the baseball game, and when I imagined her dragging
her bad leg behind her and hiding in the bushes, I almost forgot
my anger and felt sorry for her.

The mention of money was probably nothing more than a
smoke screen. Maybe the widow was jealous. In her own way, she
had been lavishing affection on the Professor for years, and to
her I was an interloper. Forbidding me to communicate with the
main house was her way of preventing me from disturbing their
relationship.

I started work again on July 7, the day known as Tanabata, the
Star Festival. The notes fluttering on the Professor's jacket as he
met me at the door reminded me of the strips of colored paper on
which children write their wishes for the festival. My portrait and
the square root sign next to it were still clipped to his cuff.

"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
^πi
+ 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
²
or log
₁₀
100.

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:

But the simplicity of the calculation only reinforces the enigma
of
e
.

To begin with, what was "natural" about this "natural logarithm"?
Wasn't it utterly unnatural to take such a number as your
base—a number that could only be expressed by a sign: this tiny e
seemed to extend to infinity, falling off even the largest sheet of paper.
I could not begin to understand this never-ending number. It
seemed as chaotic and random as a line of marching ants or a baby's
alphabet blocks, and yet it obeyed its own inner sort of logic. Perhaps
there was no fathoming God's notebooks after all. In the entire
universe there were only a handful of especially gifted human beings
able to understand a tiny part of this order, and then there were
the rest of us, who could barely appreciate their discoveries.

The book was so heavy I needed to rest my arms for a moment
before flipping back through the pages. I wondered about
Leonhard Euler, who was probably the greatest mathematician
of the eighteenth century. All I knew about him was this formula,
but reading it made me feel as though I were standing in
his presence. Using a profoundly unnatural concept, he had discovered
the natural connection between numbers that seemed
completely unrelated.

If you added 1 to e elevated to the power of π times i, you got 0:
e
^πi
+ 1 = 0.

I looked at the Professor's note again. A number that cycled on
forever and another vague figure that never revealed its true nature
now traced a short and elegant trajectory to a single point. Though
there was no circle in evidence, π had descended from somewhere
to join hands with e. There they rested, slumped against each other,
and it only remained for a human being to add 1, and the world
suddenly changed. Everything resolved into nothing, zero.

Euler's formula shone like a shooting star in the night sky, or
like a line of poetry carved on the wall of a dark cave. I slipped the
Professor's note into my wallet, strangely moved by the beauty of
those few symbols. As I headed down the library stairs, I turned
back to look. The mathematics stacks were as silent and empty as
ever—apparently no one suspected the riches hidden there.

The next day, I returned to the library to look into something else
that had been bothering me for a long time. When I found the
bound volume of the local newspaper for the year 1975, I read
through it a page at a time. The article I was looking for was in the
September 24 edition.

On September 23, at approximately 4:10 P.M., on National
Highway ... a truck belonging to a local transport company
crossed the center line, causing a head-on collision with a car ...
Professor of Mathematics ... suffered severe head injuries and
is in critical condition, while his sister-in-law, who was in the
passenger seat, is in serious condition with a broken leg. The
driver of the truck suffered only minor injuries and is being interviewed
by police, who suspect he fell asleep at the wheel.

I closed the volume, remembering the sound of the widow's
cane.