officially took two years, though in reality it never ended. At the time he began the project, the world’s most powerful supercomputers included the Cray series, the Thinking Machines arrays, the Hitachi line of supercomputers, the nCube, the Fujitsu machine, the Kendall Square Research machine, the NEC supercomputer, the Touchstone Delta, and Gregory Chudnovsky’s apartment. The apartment was a kind of container for the supercomputer at least as much as it was a container for people.
Gregory Chudnovsky’s partner in the design and construction of the supercomputer was his older brother, David Volfovich Chudnovsky. (“Volfovich” means “Son of Wolf.”) David was also a number theorist, and he lived five blocks away from Gregory. The Chudnovsky brothers were reluctant to give a name to their machine. To them, it was a household appliance that could help with their investigation of numbers. You didn’t give a name to your toaster oven, so why would you give a name to your supercomputer?
When I pressed the Chudnovsky brothers to give me some sort of a name for it, they shrugged and said it was nothing.
“I don’t want to call it nothing,” I said to the brothers.
“Why not?” David answered. However, he said, as a convenience I could refer to it as “m zero.”
At any rate, the “zero” in the machine’s name hinted at a history of failures—three previous duds in Gregory’s apartment, three homemade supercomputers that hadn’t worked. The brothers referred to these machines as negative three, negative two, and negative one. The brothers broke them up for scrap, and they got on the telephone and ordered more parts.
Whatever the supercomputer was, it filled the former living room of Gregory’s apartment, and its tentacles reached into other rooms. The brothers claimed that m zero was a “true, general-purpose supercomputer” and that it would turn out to be as fast and powerful as a Cray Y-MP. A Cray Y-MP had a sticker price of more than thirty million dollars. A Cray was a black cylinder seven feet tall, and it was cooled by liquid freon. The brothers spent around seventy thousand dollars on parts for their supercomputer, and much of the money came out of their wives’ pockets. Seventy thousand dollars was a little more than two-tenths of one percent of the cost of a Cray.
It was safe to say that Gregory Chudnovsky was one of the world’s leading architects of supercomputers. He had an ability to see the design of a supercomputer in his mind’s eye. He liked to imagine supercomputers that might never be built, like an architect who dreams of towers and cities in a splendid future. M zero was incredibly fast. Gregory called it a relativistic machine, because he had woven the design of the machine around Einstein’s theory of special relativity. M zero’s network of processors shuttled numbers around it so fast that the different parts of the machine operated in slightly different space-times.
Gregory Chudnovsky had a spare frame and a bony, handsome face. He had a long beard, streaked with gray, and dark, unruly hair, a wide forehead, and wide-spaced brown eyes. He walked in a slow, dragging shuffle, leaning on a bentwood cane, while his brother, David, typically held him under one arm, to prevent him from toppling over. He had myasthenia gravis, an autoimmune disorder of the muscles. The symptoms, in his case, were muscular weakness and difficulty in breathing. “I have to lie in bed most of the time,” Gregory told me. His condition seemed to be getting gradually worse. He developed the disease when he was twelve years old, in the city of Kiev, Ukraine, where he and David grew up. In those days, Ukraine was part of the old Soviet Union. Now Gregory spent his days sitting or lying in a bed heaped with pillows, in his bedroom down the hall from the room that housed the supercomputer. Gregory’s bedroom was filled with paper. It contained, by my estimate and the calculation of a
You almost never met one of the Chudnovsky brothers without the other. You usually found the brothers conjoined, like Siamese twins, David holding Gregory by the arm or under the armpits, speaking to him tenderly, cautioning him to be careful not to fall or hurt himself. They worked together so closely that they claimed to be a single mathematician who by chance happened to occupy two human bodies. They completed each other’s sentences and interrupted each other, but they didn’t look completely alike. While Gregory was thin and bearded, David was portly, with a plump, clean-shaven face. David’s manner was refined and aristocratic. Black-and-gray curly hair grew thickly on top of his head, and he had heavy-lidded pale blue eyes, which had a melancholy look. He always wore a starched white shirt and, usually, a muted silk necktie. His tie rested on a bulging stomach.
The Chudnovskian supercomputer, m zero, burned two thousand watts of power. It ran day and night. The brothers didn’t dare shut it down; they were afraid it would die if they did. At least twenty-five fans blew air through the machine to keep it cool; otherwise something might melt. Waste heat permeated Gregory’s apartment, and the room that contained the supercomputer climbed to more than a hundred degrees Fahrenheit in the summer. The brothers kept the apartment’s lights turned off as much as possible. If they switched on too many lights while m zero was running, they feared they might start an electrical fire. Gregory couldn’t breathe city air without developing lung trouble, so he kept the apartment’s windows closed all the time. He had air conditioners running in them during the summer, but that didn’t seem to reduce the heat. As the temperature climbed on hot days, the inside of the apartment smelled of cooking circuit boards, a sign that m zero was not well. A steady stream of boxes arrived by Federal Express, and an opposing stream of boxes flowed back to mail-order houses, containing parts that had overheated, failed, bombed, or acted strange, along with letters from the brothers demanding an exchange or their money back. The building superintendent didn’t know that the Chudnovsky brothers were using a supercomputer in Gregory’s apartment. The brothers were afraid he would find out.
The Chudnovskys, between them, had published more than a hundred and fifty papers and twelve books, mostly on the subject of number theory or mathematical physics. They lived in Kiev until 1977, when they left the Soviet Union and, accompanied by their parents, went to France. The family lived there for six months, where David fell in love with a French diplomat named Nicole Lannegrace, and they were married. The Chudnovsky brothers, along with their parents and Nicole Lannegrace, immigrated to the United States and settled in New York, where Nicole became a diplomat with the United Nations. The brothers eventually became American citizens.
The brothers enjoyed an official relationship with Columbia University: Columbia called them senior research scientists in the Department of Mathematics, but they didn’t have tenure, they didn’t teach students, and they didn’t attend faculty meetings. They were lone inventors, operating out of Gregory’s apartment. Gregory’s wife, Christine Pardo Chudnovsky, was an attorney with a midtown law firm. She had been an undergraduate at Columbia University when Gregory arrived there, and she’d fallen in love with him at first sight. Nicole Lannegrace’s salary as a U.N. diplomat and Christine’s as a lawyer helped cover much of the funding needs of the brothers’ supercomputing complex in Gregory and Christine’s apartment. Gregory and David’s mother, Malka Benjaminovna Chudnovsky, a retired engineer, was living with Gregory and Christine and was in poor health. David spent his days in Gregory’s apartment, taking care of his brother, their mother, and m zero.
When the Chudnovskys applied to leave the Soviet Union, it attracted the attention of the KGB. The brothers happened to be friends with the physicist Andrei Sakharov, a key inventor of the Soviet hydrogen bomb, who had later become a human-rights activist and a proponent of nuclear disarmament, getting himself into serious trouble with the Kremlin. The Chudnovskys’ association with Sakharov, as well as the fact that they were Jewish and mathematical, attracted at least a dozen KGB agents to their case. The brothers’ father, Volf Grigorevich Chudnovsky (“Wolf, Son of Gregory”) was severely beaten by KGB agents in 1977. Volf died in 1985, in New York City, of what the brothers believed were lingering effects of his torture. Volf Chudnovsky was a professor of civil engineering at the Kiev Architectural Institute, and he specialized in the structural stability of buildings, towers, and bridges. Not long before he died, he constructed in Gregory’s apartment a labyrinth of bookshelves, his last work of civil engineering. Volf’s bookshelves extended into every corner of the apartment, and they had become packed with literature and computer books and books on history and art and, above all, books and papers on the subject of numbers. Since almost all numbers run to infinity (in digits) and are totally unexplored, an apartment full of writings on numbers holds hardly any knowledge about numbers at all. Numbers, and the patterns of relationships among them, are powerful, deep, and mysterious. It is not at all clear that the human mind evolved in such a way that it is very much able to understand numbers. But it helps to have a supercomputer on the premises to advance the work.
ONE DAY, I called the Columbia University math department trying to find out how to make contact with the Chudnovskys. I had read a short news item about them but could learn very little that was definite. They were reportedly living somewhere in New York City. However, they did not seem to be listed in the Manhattan telephone book, and they didn’t have an unlisted telephone number, either. (I learned later that they actually were listed in
