On July 22, 1977, plainclothesmen from the K.G.B. accosted Volf and Malka on a street in Kiev and beat them up. They broke Malka’s arm and fractured her skull. David took his mother to the hospital. “The doctor in the emergency room said there was no fracture,” David said.

Gregory, at home in bed, was not so vulnerable. Also, he was conspicuous in the West. Edwin Hewitt, a mathematician at the University of Washington, in Seattle, had visited Kiev in 1976 and collaborated with Gregory on a paper, and later, when Hewitt learned that the Chudnovsky family was in trouble, he persuaded Senator Henry M. Jackson, the powerful member of the Senate Armed Services Committee, to take up the Chudnovskys’ case. Jackson put pressure on the Soviets to let the family leave the country. Just before the K.G.B. attacked the parents, two members of a French parliamentary delegation that was in Kiev made an unofficial visit to the Chudnovskys to see what was going on. One of the visitors, a staff member of the delegation, was Nicole Lannegrace, who married David in 1983. Andrei Sakharov also helped to draw attention to the Chudnovskys’ increasingly desperate situation. Two months after the parents were attacked, the Soviet government unexpectedly let the family go. “That summer when I was getting killed by the K.G.B., I could never have imagined that the next year I would be in Paris or that I would wind up in New York, married to a beautiful Frenchwoman,” David said.__ The Chudnovsky family settled in New York, near Columbia University.

If pi is truly random? then at times pi will appear to be ordered. Therefore, if pi is random it contains accidental order. For example, somewhere in pi a sequence may run 07070707070707 for as many decimal places as there are, say, hydrogen atoms in the sun. It’s just an accident. Somewhere else the same sequence of zeros and sevens may appear, only this time interrupted by a single occurrence of the digit 3. Another accident. Those and all other “accidental” arrangements of digits almost certainly erupt in pi, but their presence has never been proved. “Even if pi is not truly random, you can still assume that you get every string of digits in pi,” Gregory said.

If you were to assign letters of the alphabet to combinations of digits, and were to do this for all human alphabets, syllabaries, and ideograms, then you could fit any written character in any language to a combination of digits in pi. According to this system, pi could be turned into literature. Then, if you could look far enough into pi, you would probably find the expression “See the U.S.A. in a Chevrolet!” a billion times in a row. Elsewhere, you would find Christ’s Sermon on the Mount in His native Aramaic tongue, and you would find versions of the Sermon on the Mount that are pure blasphemy. Also, you would find a dictionary of Yanomamo curses. A guide to the pawnshops of Lubbock. The book about the sea which James Joyce supposedly declared he would write after he finished “Finnegans Wake.” The collected transcripts of “The Tonight Show” rendered into Etruscan. “Knowledge of All Existing Things,” by Ahmes the Egyptian scribe. Each occurrence of an apparently ordered string in pi, such as the words “Ruin hath taught me thus to ruminate / That Time will come and take my love away,” is followed by unimaginable deserts of babble. No book and none but the shortest poems will ever be seen in pi, since it is infinitesimally unlikely that even as brief a text as an English sonnet will appear in the first 1077 digits of pi, which is the longest piece of pi that can be calculated in this universe.

Anything that can be produced by a simple method is by definition orderly. Pi can be produced by various simple methods of rational approximation, and those methods yield the same digits in a fixed order forever. Therefore, pi is orderly in the extreme. Pi may also be a powerful random-number generator, spinning out any and all possible combinations of digits. We see that the distinction between chance and fixity dissolves in pi. The deep connection between disorder and order, between cacophony and harmony, in the most famous ratio in mathematics fascinated Gregory and David Chudnovsky. They wondered if the digits of pi had a personality.

“We are looking for the appearance of some rules that will distinguish the digits of pi from other numbers,” Gregory explained. “It’s like studying writers by studying their use of words, their grammar. If you see a Russian sentence that extends for a whole page, with hardly a comma, it is definitely Tolstoy. If someone were to give you a million digits from somewhere in pi, could you tell it was from pi? We don’t really look for patterns; we look for rules. Think of games for children. If I give you the sequence one, two, three, four, five, can you tell me what the next digit is? Even a child can do it; the next digit is six. How about this game? Three, one, four, one, five, nine. Just by looking at that sequence, can you tell me the next digit? What if I gave you a sequence of a million digits from pi? Could you tell me the next digit just by looking at the sequence? Why does pi look like a totally unpredictable sequence with the highest complexity? We need to find out the rules that govern this game. For all we know, we may never find a rule in pi.”

Herbert Robbins, the co-author of “What Is Mathematics?,” is an emeritus professor of mathematical statistics at Columbia University. For the past six years, he has been teaching at Rutgers. The Chudnovskys call him once in a while to get his advice on how to use statistical tools to search for signs of order in pi. Robbins lives in a rectilinear house that has a lot of glass in it, in the woods on the outskirts of Princeton. Some of the twentieth century’s most creative and powerful discoveries in statistics and probability theory happened inside his head. Robbins is a tall, restless man in his seventies, with a loud voice furrowed cheeks, and penetrating eyes One recent day, he stretched himself out on a daybed in a garden room in his house and played with a rubber band, making a harp across his fingertips.

“It is a very difficult philosophical question, the question of what ‘random’ is,” he said. He plucked the rubber band with his thumb, boink, boink. “Everyone knows the famous remark of Albert Einstein, that God does not throw dice. Einstein just would not believe that there is an element of randomness in the construction of the world. The question of whether the universe is a random process or is determined in some way is a basic philosophical question that has nothing to do with mathematics. The question is important. People consider it when they decide what to do with their lives. It concerns religion. It is the question of whether our fate will be revealed or whether we live by blind chance. My God, how many people have been murdered over an answer to that question! Mathematics is a lesser activity than religion in the sense that we’ve agreed not to kill each other but to discuss things.”