the Manhattan telephone book but under a nonexistent name.) “The Chudnovskys?” the person who answered the phone at Columbia said. “I have no idea where they are. We haven’t seen them around here in a long time. I have an old phone number for them. Somebody said it doesn’t work anymore.”
I dialed the number and got a fax tone. I handwrote a message on a piece of paper and faxed it, asking if this number belonged to the Chudnovskys and, if so, would they be able to meet with me? There was no reply. Weeks passed. I gave up. But then one day my phone rang; it was David Chudnovsky. “Look, you are welcome,” he said. He had a genteel-sounding voice with a Russian accent.
On a cold winter day soon afterward, I rang the bell of Gregory’s apartment on 120th Street. I was carrying a little notebook and a mechanical pencil in my shirt pocket. David answered the door. He pulled the door open a few inches, and then it stopped. It was jammed against an empty cardboard box and a mass of hanging coats. He nudged the box out of the way with his foot. “Don’t worry,” he said. “Nothing
We were standing in a long, dark hallway. The place was a swamp of heat. My face and armpits began to drip with sweat. The lights were off, and it was hard to see anything. This was the reason for David’s flashlight. The hall was lined on both sides with bookshelves supporting huge stacks of paper and books. The shelves took up most of the space, leaving a passage about two feet wide running down the length of the hallway. At the end of the hallway was a French door. Its mullioned glass panes were covered with translucent paper. The panes glowed.
We went along the hallway. We passed a bathroom and a bedroom door, which was closed. The bedroom belonged to Malka Benjaminovna Chudnovsky. We passed a sort of cave containing vast amounts of paper. This was Gregory’s bedroom, his junkyard. We passed a small kitchen, our feet rolling on computer cables. David opened the French door, and we entered the living room. This was the chamber of the supercomputer. A bare lightbulb burned in a ceiling fixture. The room contained seven display screens, two of which were filled with numbers; the other screens were turned off. The windows were closed and the shades were drawn. Gregory Chudnovsky sat on a chair facing the lit-up screens. He wore a tattered and patched lamb’s wool sweater, a starched white shirt, blue sweatpants, and the hand-stitched two-tone socks. From his toes trailed a pair of heelless leather slippers. His cane was hooked over his shoulder, hung there for convenience. “Right now, our goal is to compute pi,” he said. “For that we have to build our own computer.” He had a resonant voice and a Russian accent.
“We are a full-service company,” David said. “Of course, you know what ‘full-service’ means in New York. It means ‘You want it? You do it yourself.’”
A steel frame stood in the center of the room, screwed together with bolts. It held split-open shells of personal computers—cheap PC clones, knocked wide open like cracked walnuts, their meat spilling all over the place. The brothers had crammed superfast logic boards inside the PCs. Red lights on the boards blinked. The floor was a quagmire of cables.
The brothers had also managed to fit into the room masses of empty cardboard boxes, and lots of books (Russian classics, with Cyrillic lettering on their spines), and screwdrivers, and data-storage tapes, and software manuals by the cubic yard, and stalagmites of obscure trade magazines, and a twenty-thousand-dollar engineering computer that they no longer used. “We use it as a place to stack paper,” Gregory explained. From an oval photograph on the wall, the face of Volf Chudnovsky, their late father, looked down on the scene. The walls and the French door were covered with sheets of drafting paper showing circuit diagrams. They resembled cities seen from the air. Various disk drives were scattered around the room. The drives were humming, and there was a continuous whir of fans. A strong warmth emanated from the equipment, as if a steam radiator were going in the room. The brothers were heating the apartment with silicon chips.
“MYASTHENIA GRAVIS is a funny thing,” Gregory Chudnovsky said one day from his bed in his bedroom, the junkyard. “In a sense, I’m very lucky, because I’m alive, and I’m alive after so many years. There is no standard prognosis. It sometimes strikes young women and older women. I wonder if it is some kind of sluggish virus.”
It was a cold afternoon, and rain pelted the windows; the shades were drawn, as always, and the room was stiflingly warm. He lay against a heap of pillows with his legs folded under him. His bed was surrounded by freestanding bookshelves packed and piled with ramparts of stacked paper. That day, he wore the same tattered wool sweater, a starched white shirt, blue sweatpants, and another pair of handmade socks. I had never seen socks like Gregory’s. They were two-tone socks, wrinkled and floppy, hand-sewn from pieces of dark blue and pale blue cloth, and they looked comfortable. They were the work of Malka Benjaminovna, his mother. Lines of computer code flickered on the screen beside his bed.
This was an apartment built for long voyages. The paper in the room was jammed into bookshelves along the wall, too, from floor to ceiling. The brothers had wedged the paper, sheet by sheet, into manila folders, until the folders had grown as fat as melons. The paper was also stacked chest-high to chin-high on five chairs (three of them in a row beside his bed). It was heaped on top of and filled two steamer trunks that sat beneath the window, and the paper had accumulated in a sort of unstable-looking lava flow on a small folding cocktail table. I moved carefully around the room, fearful of triggering a paperslide, and I sat down on the room’s one empty chair, facing the foot of Gregory’s bed, my knees touching the blanket. The paper surrounded his bed like the walls of a fortress, and his bed sat at the center of the keep. I sensed a profound happiness in Gregory Chudnovsky. His happiness, it occurred to me later, sprang from the delicious melancholy of a life spent largely in bed while he explored a more perfect world that opened through the portals of mathematics into vistas beyond time or decay.
“The system of this paper is archaeological,” he said. “By looking at a slice, I know the date. This slice is from five years ago. Over here is some paper from four years ago. What you see in this room is our working papers, as well as the papers we used as references. Some of the references we pull out once in a while to look at, and then we leave them in another pile. Once, we had to make a Xerox copy of the same book three times, and we put it in three different piles, so we could be sure to find it when we needed it. There are books in there by Kipling and Macaulay. Eh, this place is a mess. Actually, when we want to find a book it’s easier to go to the library.”
Much of the paper consisted of legal pads covered with Gregory’s handwriting. His handwriting was dense and careful, a flawless minuscule written with a felt-tipped pen. The writing contained a mixture of theorems, calculations, proofs, and conjectures concerning numbers. He used a felt-tip pen because he didn’t have enough strength in his hand to press a pencil on paper. Mathematicians who had visited Gregory Chudnovsky’s bedroom had come away dizzy, wondering what secrets the scriptorium might hold. He cautiously referred to the steamer trunks beneath the window as valises. They were filled to the lids with compressed paper. When Gregory and David flew to Europe to speak at conferences on the subject of numbers, they took both “valises” with them, in case they needed to refer to a proof or a theorem. Their baggage particularly annoyed Belgian officials. “The Belgians were always fining us for being overweight,” Gregory said.
The brothers’ mail-order supercomputer made their lives more convenient. It performed inhumanly difficult algebra, finding roots of gigantic systems of equations, and it constructed colored images of the interior of Gregory Chudnovsky’s body. They used the supercomputer to analyze and predict fluctuations in the stock market. They had been working with a well-known Wall Street investor named John Mulheren, helping him get a profitable edge in computerized trades on the stock market. One day I called John Mulheren to find out what the brothers had been doing for him. “Gregory and David have certainly made us money,” Mulheren said, but he wouldn’t give any details on what the brothers had done. Mulheren had been paying the Chudnovskys out of his trading profits; they used the money to help fund their research into numbers. To them, numbers were more beautiful, more nearly perfect, possibly more complicated, and arguably more real than anything in the world of physical matter.
THE NUMBER PI, or ?, is the most famous ratio in mathematics. It is also one of the most ancient numbers known to humanity. Nobody knows when pi first came to the awareness of the human species. Pi may very well have been known to the builders of Stonehenge, around 2,600 B.C.E. Certainly it was known to the ancient Egyptians. Pi is approximately 3.14—it is the number of times that a circle’s diameter will fit around a circle. On the following page is a circle with its diameter.
