The Man Who Loved Only Numbers

The Story of Paul Erdös and the Search for Mathematical Truth

Paul Erdös was one of the most prolific and eccentric mathematician of our time, a man who possessed unimaginable powers of thought yet was unable to manage some of the simplest daily tasks. He forsook all creature comforts—including a home, a mate, and a family—to pursue his lifelong study of numbers. For more than two decades, he lived out of two tattered suitcases, crisscrossing four continents at a frenzied pace, showing up uninvited on the doorsteps of colleagues, chasing mathematical problems in pursuit of lasting beauty and ultimate truth. He was the houseguest from hell. He couldn't drive. He couldn't cook. He didn't even know how to boil water for tea. His mother had tied his shoes for him until he was eleven, and he buttered his first piece of toast at the age of 21.

In this bestselling biography, Hoffman provides an intimate look at Erdös's life, introducing readers to a cast of remarkable geniuses, from Archimedes to Stanislaw Ulam, one of the chief minds behind the Los Alamos nuclear project. Drawing on years of interviews with Erdös and his friends and devoted collaborators, Hoffman has composed a vibrant portrait of the impish philosopher-scientist whose accomplishments continue to enrich and inform our world.

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"Paul Hoffman, in this marvelous biography gives us a vivid and strangely moving—portrait of this singular creature, one that brings out not only Erdös's genius and his oddness, but his warmth and sense of fun, the joyfulness of his strange life." —Oliver Sacks

"One of the most captivating books I have read in years... a completely absorbing fast-paced memoir." —Kay Redfield Jamison, The Washington Post

"A funny, marvelously readable portrait of one of the most brilliant and eccentric men in history." —Seattle Times

"This book opens doors on a world and characters that are often invisible." —The New York Times Book Review


Végre nem butulok tovább
(Finally I am becoming stupider no more)
—the epitaph Paul Erdös wrote for himself

It was dinnertime in Greenbrook, New Jersey, on a cold spring day in 1987, and Paul Erdös, then seventy-four, had lost four mathematical colleagues, who were sitting fifty feet in front of him, sipping green tea. Squinting, Erdös scanned the tables of the small Japanese restaurant, one arm held out to the side like a scarecrow's. He was angry with himself for letting his friends slip out of sight. His mistake was to pause at the coat check while they charged ahead. His arm was flapping wildly now, and he was coughing. "I don't understand why the SF has seen fit to send me a cold," he wheezed. (The SF is the Supreme Fascist, the Number-One Guy Up There, God, who was always tormenting Erdös by hiding his glasses, stealing his Hungarian passport, or, worse yet, keeping to Himself the elegant solutions to all sorts of intriguing mathematical problems.) "The SF created us to enjoy our suffering," Erdös said. "The sooner we die, the sooner we defy His plans."

Erdös still didn't see his friends, but his anger dissipated--his arm dropped to his side--as he heard the high-pitched squeal of a small boy, who was dining with his parents. "An epsilon!" Erdös said. (Epsilon was Erdös's word for a small child; in mathematics that Greek letter is used to represent small quantities.) Erdös moved slowly toward the child, navigating not so much by sight as by the sound of the boy's voice. "Hello," he said, as he reached into his ratty gray overcoat and extracted a bottle of Benzedrine. He dropped the bottle from shoulder height and with the same hand caught it a split second later. The epsilon was not at all amused, but perhaps to be polite, his parents made a big production of applauding. Erdös repeated the trick a few more times, and then he was rescued by one of his confederates, Ron Graham, a mathematician at AT&T, who called him over to the table where he and Erdös's other friends were waiting.

The waitress arrived, and Erdös, after inquiring about each item on the long menu, ordered fried squid balls. While the waitress took the rest of the orders, Erdös turned over his placemat and drew a tiny sketch vaguely resembling a rocket passing through a hula-hoop. His four dining companions leaned forward to get a better view of the world's most prolific mathematician plying his craft. "There are still many edges that will destroy chromatic number three," Erdös said. "This edge destroys bipartiteness." With that pronouncement Erdös closed his eyes and seemed to fall asleep.

Mathematicians, unlike other scientists, require no laboratory equipment--a practice that reportedly began with Archimedes, who, after emerging from his bath and rubbing himself with olive oil, discovered the principles of geometry by using his fingernails to trace figures on his oily skin. A Japanese restaurant, apparently, is as good a place as any to do mathematics. Mathematicians need only peace of mind and, occasionally, paper and pencil. "That's the beauty of it," Graham said. "You can lie back, close your eyes, and work. Who knows what problem Paul's thinking about now?"

"There was a time at Trinity College, in the 1930s I believe, when Erdös and my husband, Harold, sat thinking in a public place for more than an hour without uttering a single word," recalled Anne Davenport, the widow of one of Erdös's English collaborators. "Then Harold broke the long silence, by saying, 'It is not naught. It is one.' Then all was reflief and joy. Everyone around them thought they were mad. Of course, they were."

Before Erdös died, on September 20, 1996, at the age of eighty-three, he had managed to think about more problems than any other mathematician in history. He wrote or co-authored 1,475 academic papers, many of them monumental, and all of them substantial. It wasn't just the quantity of work that was impressive but the quality: "There is an old saying," said Erdös. "Non numerantur, sed ponderantur (They are not counted but weighed). In the old [Hungarian] parliament of noblemen, they didn't count the votes: they weighed them. And this is true of papers. You know, Riemann had a very short list of papers, Gödel had a short list. Gauss was very prolific, as was Euler, of course." Even in his seventies there were years when Erdös published 50 papers, which is more than most good mathematicians write in a lifetime. He proved that mathematics isn't just a young man's game.

Erdös (pronounced "air-dish") structured his life to maximize the amount of time he had for mathematics. He had no wife or children, no job, no hobbies, not even a home, to tie him down. He lived out of a shabby suitcase and a drab orange plastic bag from Centrum Aruhaz ("Central Warehouse"), a large department store in Budapest. In a never-ending search for good mathematical problems and fresh mathematical talent, Erdös crisscrossed four continents at a frenzied pace, moving from one university or research center to the next. His modus operandi was to show up on the doorstep of a fellow mathematician, declare, "My brain is open," work with his host for a day or two, until he was bored or his host was run down, and then move on to another home.

Erdös's motto was not "Other cities, other maidens" but "Another roof, another proof." He did mathematics in more than 25 different countries, completing important proofs in remote places and sometimes publishing them in equally obscure journals. Hence the limerick, composed by one of his colleagues:

A conjecture both deep and profound
Is whether the circle is round.
In a paper of Erdös
Written in Kurdish
A counterexample is found.
When Erdös heard the limerick, he wanted to publish a paper in Kurdish but couldn't find a Kurdish math journal.

Erdös first did mathematics at the age of three, but for the last 25 years of his life, since the death of his mother, he put in nineteen-hour days, keeping himself fortified with ten to twenty milligrams of Benzedrine or Ritalin, strong espresso, and caffeine tablets. "A mathematician," Erdös was fond of saying, "is a machine for turning coffee into theorems." When friends urged him to slow down, he always had the same response: "There'll be plenty of time to rest in the grave."

Erdös would let nothing stand in the way of mathematical progress. When the name of a colleague in California came up at breakfast in New Jersey, Erdös remembered a mathematical result he wanted to share with him. He headed toward the phone and started to dial. His host interrupted him, pointing out that it was 5:00 A.M. on the West Coast.

"Good," Erdös said, "that means he'll be home." When challenged further in situations like this, Erdös was known to respond, "Louis the Fourteenth said, 'I am the state'; Trotsky could have said, 'I am society'; and I say, 'I am reality.'" No one who knew him would disagree. "Erdös had a childlike tendency to make his reality overtake yours," a friend said. "And he wasn't an easy houseguest. But we all wanted him around—for his mind. We all saved problems up for him."

To communicate with Erdös you had to learn his language. "When we met," said Martin Gardner, the mathematical essayist, "his first question was 'When did you arrive?' I looked at my watch, but Graham whispered to me that it was Erdös's way of asking, 'When were you born?'" Erdös often asked the same question another way: "When did the misfortune of birth overtake you?" His language had a special vocabulary—not just "the SF" and "epsilon" but also "bosses" (women), "slaves" (men), "captured" (married), "liberated" (divorced), "recaptured" (remarried), "noise" (music), "poison" (alcohol), "preaching" (giving a mathematics lecture), "Sam" (the United States), and "Joe" (the Soviet Union). When he said someone had "died," Erdös meant that the person had stopped doing mathematics. When he said someone had "left," the person had died.

At five foot six, 130 pounds, Erdös had the wizened, cadaverous look of a drug addict, but friends insist he was frail and gaunt long before he started taking amphetamines. His hair was white, and corkscrew-shaped whiskers shot out at odd angles from his face. He usually wore a gray pinstriped jacket, dark trousers, a red or mustard shirt or pajama top, and sandals or peculiar pockmarked Hungarian leather shoes, made especially for his flat feet and weak tendons. His whole wardrobe fit into his one small suitcase, with plenty of room left for his dinosaur of a radio. He had so few clothes that his hosts found themselves washing his socks and underwear several times a week. "He could buy more," one of his colleagues said, "or he could wash them himself. I mean, it takes zero IQ to learn how to operate a washing machine." But if it wasn't mathematics, Erdös wouldn't be bothered. "Some French socialist said that private property was theft," Erdös recalled. "I say that private property is a nuisance."

The only possessions that mattered to him were his mathematical notebooks. He filled ten of them by the time he died. He always carried one around with him, so that he could record his mathematical insights on a moment's notice. "Erdös came to my twins' bar mitzvah, notebook in hand," said Peter Winkler, a colleague of Graham's at AT&T. "He also brought gifts for my children--he loved kids--and behaved himself very well. But my mother in law tried to throw him out. She thought he was some guy who wondered in off the street, in a rumpled suit, carrying a pad under his arm. It is entirely possible that he proved a theorem or two during the ceremony."

All of his clothes, including his socks and custom-made underwear, were silk, because he had an undiagnosed skin condition that was aggravated by other kinds of fabric. He didn't like people to touch him. If you extended your hand, he wouldn't shake it. Instead, he'd limply flop his hand on top of yours. "He hated it if I kissed him," said Magda Fredro, a first cousin who was otherwise very close to him. "And he'd wash his hands fifty times a day. He got water everywhere. It was hell on the bathroom floor."

Although Erdös avoided physical intimacy, and was always celibate, he was friendly and compassionate. "He existed on a web of trust," said Aaron Meyerowitz, a mathematician at Florida Atlantic University. "When I was a graduate student and we had never met before, I gave him a ride. I didn't know the route and asked him if he wanted to navigate with a map. He didn't want to [and probably didn't know how to]. He just trusted that I, a total stranger, would get him there."

What little money Erdös received in stipends or lecture fees, he gave away to relatives, colleagues, students, and strangers. He could not pass a homeless person without giving him money. "In the early 1960s, when I was a student at University College London," recalled D. G. Larman, "Erdös came to visit us for a year. After collecting his first month's salary he was accosted by a beggar on Euston station, asking for the price of a cup of tea. Erdös removed a small amount from the pay packet to cover his own frugal needs and gave the remainder to the begger." In 1984 he won the prestigious Wolf prize, the most lucrative award in mathematics. He contributed most of the $50,000 he received to a scholarship in Israel he established in the name of his parents. "I kept only seven hundred and twenty dollars," Erdös said, "and I remember someone commenting that for me even that was a lot of money to keep." Whenever Erdös learned of a good cause--a struggling classical-music radio station, a fledgling Native American movement, a camp for wayward boys--he promptly made a small donation. "He's been gone a year, "said Graham, " and I'm still getting mail from organizations he gave donations to. Today I got a postcard from an Israeli girls' home."

In the late 1980s Erdös heard of a promising high school student named Glen Whitney who wanted to study mathematics at Harvard but was a little short the tuition. Erdös arranged to see him and, convinced of the young man's talent, lent him $1,000. He asked Whitney to pay him back only when it would not cause financial strain. A decade later Graham heard from Whitney, who at last had the money to repay Erdös. "Did Erdös expect me to pay interest?" Whitney wondered. "What should I do?" he asked Graham. Graham talked to Erdös. "Tell him," Erdös said, "to do with the $1,000 what I did."

Erdös was a mathematical prodigy. At three he could multiply three-digit numbers in his head, and at four he discovered negative numbers. "I told my mother," he recalled, "that if you take two hundred and fifty from a hundred you get minus a hundred and fifty. My second great discovery was death. Children don't think they're ever going to die. I was like that too, until I was four. I was in a shop with my mother and suddenly I realized I was wrong. I started to cry. I knew I would die. From then on I've always wanted to be younger. In 1970 I preached in Los Angeles on 'my first two-and-a-half billion years in mathematics.' When I was a child, the earth was said to be two billion years old. Now scientists say it's four and a half billion. So that makes me two-and-a-half billion. The students at the lecture drew a time line that showed me riding a dinosaur. I was asked, 'How were the dinosaurs?' Later, the right answer occurred to me: 'You know, I don't remember, because an old man only remembers the very early years, and the dinosaurs were born yesterday, only a hundred million years ago.'"

Erdös loved the dinosaur story and repeated it again and again in his mathematical talks. "He was the Bob Hope of mathematics, a kind of vaudeville performer who told the same jokes and the same stories a thousand times," said Melvyn Nathanson at a mathematical memorial service for Erdös in Budapest. "When he was scheduled to give yet another talk, no matter how tired he was, as soon as he was introduced to an audience, the adrenaline (or maybe amphetamine) would release into his system and he would bound onto the stage, full of energy, and do his routine for the 1,001-st time."

In the early 1970s Erdös started appending the initials P.G.O.M. to his name, which stood for Poor Great Old Man. When he turned sixty, he became P.G.O.M.L.D., the L.D. for Living Dead. At sixty-five he graduated to P.G.O.M.L.D.A.D., the A.D. for Archaeological Discovery. At seventy he became P.G.O.M.L.D.A.D.L.D., the L.D. for Legally Dead. And at seventy-five he was P.G.O.M.L.D.A.D.L.D.C.D., the C.D. for Counts Dead. In 1987, when he was 74, he explained: "The Hungarian Academy of Sciences has two hundred members. When you turn seventy-five, you can stay in the academy with full privileges, but you no longer count as a member. That's why the C.D. Of course, maybe I won't have to face that emergency. They are planning an international conference for my seventy-fifth birthday. It may have to be for my memory. I'm miserably old. I'm really not well. I don't understand what's happening to my body--maybe the final solution."