Authors: Richard Preston

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referred to as the Eddington machine.

The Eddington machine was the entire universe turned into a computer. It was made of all the atoms in the universe. If the Chudnovsky brothers could figure out how to program it with FORTRAN , they 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. To be realistic, the brothers felt that a practical Eddington machine wouldn’t be able to store more than about 10 77 digits of pi. That’s only a hundredth of the Eddington number. Now, what if the digits of pi were to begin to show regularity only beyond 10 77 digits? Suppose, for example, that pi were only to begin manifesting a regularity starting at 10 100 decimal places? That number is known as a googol. If the design in pi appeared only after a googol of digits, then not even the largest possible computer would ever be able to penetrate pi far enough to reveal any order in it. Pi would look totally disordered to the universe, even if it contained a slow, vast, delicate structure. A mere googol of pi might be only the first warp and weft, the first knot in a colored thread, in a limitless tapestry woven into gardens of delight and cities and towers and unicorns and unimaginable beasts and impenetrable mazes and unworldly cosmogonies, all invisible forever to us. It may never be possible, in principle, to see the design in the digits of pi. Not even nature itself may know the nature of pi.

“If pi doesn’t show systematic behavior until more than ten to the seventy-seven decimal places, it would really be a disaster,” Gregory said. “It would actually be horrifying.”

“I wouldn’t give up,” David said. “There might be some way of leaping over the barrier—”

“And of attacking the son of a bitch,” Gregory said.

T HE BROTHERS first came in contact with the membrane that divides the dreamlike earth from the perfect and beautiful world of mathematical reality when they were boys, growing up in Kiev. Their father, Volf, gave David a book entitled What is Mathematics?, written by Richard Courant and Herbert Robbins, two American mathematicians. The book is a classic. Millions of copies of it had been printed in unauthorized Russian and Chinese editions alone. (Robbins wrote most of the book, while Courant got ownership of the copyright and collected most of the royalties but paid almost none of the money to Robbins.) After reading it, David decided to become a mathematician. Gregory soon followed his brother’s footsteps into the nature beyond nature.

Gregory’s first publication, in a Soviet math journal, came when he was sixteen years old: “Some Results in the Theory of Infinitely Long Expressions.” Already you can see where he was headed. David, sensing his younger brother’s power, encouraged him to grapple with central problems in mathematics. In 1900, at the dawn of the twentieth century, the German mathematician David Hilbert had proposed a series of twenty-three great problems in mathematics that remained to be solved, and he’d challenged his colleagues, and future generations, to solve them. They became known as the Hilbert problems. At the age of seventeen, Gregory Chudnovsky made his first major discovery when he solved Hilbert’s Tenth Problem. To solve a Hilbert problem would be an achievement for a lifetime; Gregory was a high school student who had read a few books on mathematics. Strangely, a young Russian mathematician named Yuri Matyasevich had also just solved Hilbert’s Tenth Problem, but Gregory hadn’t heard the news. Eventually, Matyasevich said that the Chudnovsky method was the preferred way to solve Hilbert’s Tenth Problem.

The brothers enrolled at Kiev State University, and took their PhDs at the Ukrainian Academy of Sciences. At first, they published their papers separately, but as Gregory’s health declined, they began collaborating. They lived with their parents in Kiev

The Eddington machine was the entire universe turned into a computer. It was made of all the atoms in the universe. If the Chudnovsky brothers could figure out how to program it with FORTRAN , they 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. To be realistic, the brothers felt that a practical Eddington machine wouldn’t be able to store more than about 10 77 digits of pi. That’s only a hundredth of the Eddington number. Now, what if the digits of pi were to begin to show regularity only beyond 10 77 digits? Suppose, for example, that pi were only to begin manifesting a regularity starting at 10 100 decimal places? That number is known as a googol. If the design in pi appeared only after a googol of digits, then not even the largest possible computer would ever be able to penetrate pi far enough to reveal any order in it. Pi would look totally disordered to the universe, even if it contained a slow, vast, delicate structure. A mere googol of pi might be only the first warp and weft, the first knot in a colored thread, in a limitless tapestry woven into gardens of delight and cities and towers and unicorns and unimaginable beasts and impenetrable mazes and unworldly cosmogonies, all invisible forever to us. It may never be possible, in principle, to see the design in the digits of pi. Not even nature itself may know the nature of pi.

“If pi doesn’t show systematic behavior until more than ten to the seventy-seven decimal places, it would really be a disaster,” Gregory said. “It would actually be horrifying.”

“I wouldn’t give up,” David said. “There might be some way of leaping over the barrier—”

“And of attacking the son of a bitch,” Gregory said.

T HE BROTHERS first came in contact with the membrane that divides the dreamlike earth from the perfect and beautiful world of mathematical reality when they were boys, growing up in Kiev. Their father, Volf, gave David a book entitled What is Mathematics?, written by Richard Courant and Herbert Robbins, two American mathematicians. The book is a classic. Millions of copies of it had been printed in unauthorized Russian and Chinese editions alone. (Robbins wrote most of the book, while Courant got ownership of the copyright and collected most of the royalties but paid almost none of the money to Robbins.) After reading it, David decided to become a mathematician. Gregory soon followed his brother’s footsteps into the nature beyond nature.

Gregory’s first publication, in a Soviet math journal, came when he was sixteen years old: “Some Results in the Theory of Infinitely Long Expressions.” Already you can see where he was headed. David, sensing his younger brother’s power, encouraged him to grapple with central problems in mathematics. In 1900, at the dawn of the twentieth century, the German mathematician David Hilbert had proposed a series of twenty-three great problems in mathematics that remained to be solved, and he’d challenged his colleagues, and future generations, to solve them. They became known as the Hilbert problems. At the age of seventeen, Gregory Chudnovsky made his first major discovery when he solved Hilbert’s Tenth Problem. To solve a Hilbert problem would be an achievement for a lifetime; Gregory was a high school student who had read a few books on mathematics. Strangely, a young Russian mathematician named Yuri Matyasevich had also just solved Hilbert’s Tenth Problem, but Gregory hadn’t heard the news. Eventually, Matyasevich said that the Chudnovsky method was the preferred way to solve Hilbert’s Tenth Problem.

The brothers enrolled at Kiev State University, and took their PhDs at the Ukrainian Academy of Sciences. At first, they published their papers separately, but as Gregory’s health declined, they began collaborating. They lived with their parents in Kiev