The Chudnovsky brothers yearned to probe the mystery of pi, so they built their own supercomputer out of mail-order parts. NewYorkerArchive
What is your name?. . . Bob. Fine. O.K. So it’s two hundred and fifty- seven dollars plus twenty-nine dollars for Federal Express?”
“Do you want my MasterCard? Look, it’s really imperative that I get my unit tomorrow. A.K., please, I really need my unit bad.” David hung up the telephone and sighed. “This is what has happened to a pure mathematician.” In the junk yard, his nest, his paper-lined oubliette, Gregory kicked off hi gentleman’s slippers, lay down on the bed, and predicted the future. He said “The gigaflop supercomputers of today are almost useless. What is needed is a teraflop machine. That’s a machine that can run at a trillion flops, a trillion floating-point operations per second, or roughly a thousand times as fast as Cray Y-MP8. One such design for teraflop machine, by Monty Denneau at I.B.M.
The square root of two is an irrational number. There is simply no way to represent any irrational number as the ratio of two whole numbers; it can’t be done. Hippasus of Metapontum supposedly made this discovery in the fifth century B.C., while travelling in a boat with some mathematicians who were followers of Pythagoras.
You can take the Leibniz series out a long distance—you can even dramatically speed up its movement toward pi by adding a few corrections to it—but no matter how far you take the Leibniz series, and no matter how many corrections you hammer into it, when you stop the operation and sum the terms, you will get anumber that is somewhere around pi but is not pi, and you will be damned if you can put your hands on pi.
In 1873, Georg Cantor, a Russian-born mathematician who was one of the towering intellectual figures of the nineteenth century, proved that the set of transcendental numbers is infinitely more extensive than the set of algebraic numbers. That is, finite algebra can’t find or describe most numbers. To put it another way, most numbers are infinitely long and non-repeating in any rational form of representation. In this respect, most numbers are like pi.
“Pi is a damned good fake of a random number,” Gregory said. “I just wish it were not as good a fake. It would make our lives a lot easier.” The Eddington machine would be the universal supercomputer. It would be made of all the atoms in the universe. The Eddington machine would contain ten vigintsextillion parts, and if the Chudnovsky brothers could figure out how to program it withthey might make it churn toward pi. “In order to study the sequence of pi, you have to store it in the Eddington machine’s memory,” Gregory said.
The K.G.B. began tailing the brothers. “Gregory would not believe me until it became totally obvious,” David said. “I had twelve K.G.B. agents on my tail. No, look, I’m not kidding! They shadowed me around the clock in two cars, six agents in each car. Three in the front seat and three in the back seat. That was how the K.G.B. operated.” One day, in 1976, David was walking down the street when K.G.B. officers attacked him, breaking his skull.
“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.
“Mathematics is broken into tiny specialties today, but Gregory Chudnovsky is a generalist who knows the whole of mathematics as well as anyone,” he said as he moved around. “You have to go back a hundred years, to David Hilbert, to find a mathematician as broadly knowledgeable as Gregory Chudnovsky. He’s like Mozart: he’s the last of his breed. I happen to think the brothers’ pi project is a will-o’-the-wisp, and is one of the least interesting things they’ve ever done.
The brothers’ mode of existence has come to be known among mathematicians as the Chudnovsky Problem. Herbert Robbins eventually decided that it was time to ask the entire American mathematics profession why it could not solve the Chudnovsky Problem. Robbins is a member of the National Academy of Sciences, and in 1986 he sent a letter to all of the mathematicians in the academy:
An emotional reaction to Robbins’ campaign on behalf of the Chudnovskys came a bit later from Edwin Hewitt, the mathematician who had helped get the family out of the Soviet Union, and one of the few Americans who has ever worked with Gregory Chudnovsky. Hewitt wrote to colleagues, “I have collaborated with many excellent mathematicians . . . but with no one else have I witnessed an outpouring of mathematics like that from Gregory. He simplyThe Chudnovsky situation is a national disgrace.
“Abhorrent—yes, most mathematicians would probably agree with that,” said Dale Brownawell, a respected number theorist at Penn State. “Tastes change, though. If something were to begin to show up in the digits of pi, it would boggle everyone’s mind.” Brownawell met the Chudnovskys at the Vienna airport when they escaped from the Soviet Union. “They didn’t bring much with them, just a pile of bags and boxes. David would walk through a wall to do what is right for and his brother.
“Yes, you just make a decree, Gregory said. “Anyway, this sort of talk moves into philosophical questions. What is life, and where does the money come from?” He shrugged.
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