The Last Theorem

THE SECOND PREAMBLE

There are two things in my life that I think have a bearing on the subject matter of this book, so perhaps this would be a good time to set them down.

The first: By the time I was in my early thirties, I had been exposed to a fair amount of mathematics—algebra, geometry, trigonometry, a little elementary calculus—either at Brooklyn Tech, where for a brief period in my youth I had the mistaken notion that I might become a chemical engineer, or, during World War II, in the U.S. Air Force Weather School at Chanute Field in Illinois, where the instructors tried to teach me something about the mathematical bases of meteorology.

None of those kinds of math made a great impression on me. What changed that, radically and permanently, was an article in Scientific American in the early 1950s that spoke of a sort of mathematics I had never before heard of. It was called “number theory.” It had to do with describing and cataloging the properties of that basic unit of all mathematics, the number, and it tickled my imagination.

I sent my secretary out to the nearest bookstore to buy me copies of all the books cited in the article, and I read them, and I was addicted. Over the next year and more I spent all the time I could squeeze out of a busy life in scribbling interminable calculations on ream upon ream of paper. (We’re talking about the 1950s, remember. No computers. Not even a pocket calculator. If I wanted to try factoring a number that I thought might be prime, I did it the way Fermat or Kepler or, for that matter, probably old Aristarchus himself had done it, which is to say, by means of interminably repetitious and laborious handwritten arithmetic.)

I never did find Fermat’s lost proof, or solve any other of the great mathematical puzzles. I didn’t even get very far with the one endeavor that, I thought for a time, I might actually make some headway with, namely, finding a formula for generating prime numbers. What I did accomplish—and little enough it is, for all that work—was to invent a couple of what you might call mathematical parlor tricks. One was a technique for counting on your fingers. (Hey, anybody can count on his fingers, you say. Well, sure, but up to 1,023?) The other was accomplishing an apparently impossible task.

I’ll give you the patter that goes with that trick:

If you draw a row of coins, it doesn’t matter how long a row, I will in ten seconds or less write down the exact number of permutations (heads-tails-heads, heads-tails-tails, etc.) that number of coins produces when flipped. And just to make it a little tougher on me, I will do it even if you cover up as many coins in the row as you like, from either end, so that I won’t be able to tell how many there are in the row.

Impossible, right? Care to try to figure it out? I’ll come back to you on this, but not right away.

The second thing that I think might be relevant happened some twenty years later, when I found myself for the first time in my life spending a few weeks in the island empire of Japan. I was there as a guest of Japanese science-fiction fandom, and so was Brian Aldiss, representing Britain, Yuli Kagarlitski, representing what then was still the Union of Soviet Socialist Republics, Judith Merril, representing Canada, and Arthur C. Clarke, representing Sri Lanka and most of the rest of the inhabited parts of the earth. Along with a contingent of Japanese writers and editors, the bunch of us had been touring Japanese cities, lecturing, being interviewed, and, on request, showing our silly sides. (Arthur did a sort of Sri Lankan version of a Hawaiian hula. Brian got involved in trying to pronounce a long list of Japanese words, most of which—for our hosts loved a good prank—turned out to be violently obscene. I won’t tell you what I did.) For a reward we were all treated to a decompressing weekend on Lake Biwa, where we lounged about in our kimonos and depleted the hotel’s bar.

We spent most of the time catching one another up on what we’d been doing since the last time we had been together. I thought Judy Merril had the most interesting story to tell. She had come early to Japan, and had sneaked a couple of days in Hiroshima before the rest of us had arrived. She was good at describing things, too, and she kept us interested while she told us what she had seen. Well, everyone knows about the twisted ironwork the Japanese preserved as a memorial when every other part of that building had been blown away by that first-ever-deployed-in-anger nuclear bomb, and about the melted-down face on the stone Buddha. And everyone knows about—the one that nobody can forget once that picture enters their minds—the shadow of a man that had been permanently etched, onto the stone stairs where he had been sitting, by the intolerably brilliant nuclear blast from the overhead sky.

“That must have been bright,” someone said—I think Brian.

Arthur said, “Bright enough that it could have been seen by a dozen nearby stars by now.”

“If anyone lives there to be looking,” someone else said—I think it was me.

And, we agreed, maybe someone might indeed be looking…or at least it was pretty to think so.

As to those mathematical parlor tricks:

I don’t think I should explain them to you just yet, but I promise that before this book is ended, someone will.

That someone will probably be a bright young man named Ranjit Subramanian, whom you are bound to meet in just a few pages.

After all, this book is basically Ranjit’s story.