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Joined: 23 Apr 2009, 14:52 Posts: 2539 Location: Tvashtar Paterae
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A math genius who died as a virgin.
The man who loved numbers
Paul Erdös was the world's most prolific mathematician. With no job, no home and his few clothes in an orange carrier bag, he would arrive at colleagues' houses, declare 'My brain is open' and stay. His fuel was Benzedrine and espresso, his motto was 'Another roof, another proof'. Paul Hoffman tells his amazing story
IT was dinnertime in Greenbrook, New Jersey, on a cold spring day in 1987 and Paul Erdös, then 74, had lost four mathematical colleagues, who were sitting 50ft 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, 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," said Erdös. "The sooner we die, the sooner we defy His plans."
Erdös still did not 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!" said Erdös. (Epsilon was Erdös's word for a small child; in mathematics that Greek letter is used to represent small quantities.) Erdös moved slowly towards 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 grey 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, Ronald Graham, a mathematician at the American phone company AT&T, who called him over to the table where he and Erdös's other friends were waiting. Graham was not only Erdös's friend and colleague but his minder; of necessity, he handled all his finances and correspondence.
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 place mat 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," said Erdös. "This edge destroys bipartiteness." With that pronouncement, Erdös closed his eyes and seemed to fall asleep.
Mathematicians, unlike other scientists, require no laboratory equipment - Archimedes, 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.
Anne Davenport, the widow of one of Erdös's English collaborators, remembers a time at Trinity College, in the Thirties. "Erdös and my husband, Harold, sat thinking in a public place for more than an hour without uttering a single word. Then Harold broke the long silence, by saying: 'It is not nought. It is one.' Then all was relief and joy. Everyone around them thought they were mad. Of course, they were."
Before Erdös died in 1996, at the age of 83, 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. Even in his seventies, there were years when Erdös published 50 papers, which is more than most good mathematicians write in a lifetime.
Erdös (pronounced "air-dish") structured his life to maximise 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 criss-crossed four continents at a frenzied pace, moving from one university or research centre 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 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 counter example is found.
When Erdös heard the limerick, he wanted to publish a paper in Kurdish, but couldn't find a Kurdish maths 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 19-hour days, keeping himself fortified with 10 to 20 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 towards the phone and started to dial. His host interrupted him, pointing out that it was 5am on the West Coast. "Good," said Erdös, "that means he'll be home."
"Erdös had a childlike tendency to make his reality overtake yours," said one colleague. "And he wasn't an easy house guest. But we all wanted him around - for his mind. We all saved up problems for him."
To communicate with Erdös, you had to learn his language. "When we met, his first question was: 'When did you arrive?'," said Martin Gardner, a mathematical essayist. "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 5ft 6in and 130 lb, 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 went white, and corkscrew-shaped whiskers shot out at odd angles from his face.
He usually wore a grey pin-striped jacket, dark trousers, a red or mustard shirt or pyjama top, and sandals or peculiar pockmarked Hungarian leather shoes, made especially for his flat feet and weak tendons.
His whole wardrobe fitted 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. If it wasn't mathematics, Erdös wouldn't be bothered. "Some French socialist said that private property was theft," recalled Erdös. "I say that private property is a nuisance."
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 close to him. "And he'd wash his hands 50 times a day. He got water everywhere. It was hell on the bathroom floor."
Although Erdös avoided physical intimacy and was apparently celibate, he was friendly and compassionate. What little money he 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 beggar." In 1984 he won the 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 $720," said Erdös, "and I remember someone commenting that for me even that was a lot of money to keep."
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 of the tuition fees. 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 asked Graham. "What should I do?" Graham talked to Erdös. "Tell him," said Erdös, "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 250 from 100, you get -150.
"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 realised 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 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 on to the stage, full of energy, and do his routine for the thousand and first time."
In the early 1970s, Erdös appended the initials PGOM to his name, which stood for Poor Great Old Man. When he turned 60, he became PGOMLD, the LD for Living Dead. At 65, he graduated to PGOMLDAD, the AD for Archaeological Discovery.
At 70, he became PGOMLDADLD, the LD for Legally Dead. And, at 75, he was PGOMLDADLDCD, the CD for Counts Dead (he explained that after the age of 75 you no longer count as a member of the Hungarian Academy of Sciences).
When Paul Turan, his closest friend, with whom he had written 30 papers, died in 1976, Erdös had an image of the SF assessing the work he had done with collaborators.
On one side of a balance, the SF would place the papers Erdös had co-authored with the dead; on the other side, the papers written with the living. "When the dead side tips the balance," said Erdös, "I must die too." He paused for a moment and then added: "It's just a joke of mine."
Perhaps. But for decades Erdös vigorously sought out new, young collaborators and ended many working sessions with the remark: "We'll continue tomorrow if I live."
With 485 co-authors, Erdös collaborated with more people than any other mathematician in history. Those lucky 485 are said to have an Erdös number of one, a coveted code phrase in the mathematics world for having written a paper with the master himself.
If your Erdös number is two, it means you have published with someone who has published with Erdös. If your Erdös number is three, you have published with someone who has published with someone who has published with Erdös. Einstein had an Erdös number of two.
"I was told several years ago that my Erdös number was seven," one mathematician wrote in 1969. "But it has been lowered to three.
"Last year I saw Erdös in London . . . When I told him the good news that my Erdös number had just been lowered, he expressed regret that he had to leave London that day. Otherwise, an ultimate lowering might have been accomplished."
Although he was confident of his skill in mathematics, outside that arcane world Erdös was very nearly helpless. After his mother's death, the responsibility of looking after him fell chiefly to Ronald Graham, who spent almost as much time in the 1980s handling Erdös's affairs as he did overseeing the 70 mathematicians, statisticians and computer scientists at AT&T Bell Labs.
Graham was the one who called Washington when the SF stole Erdös's visa; and during Erdös's last few years, he said: "The SF struck with increasing frequency." Graham also managed Erdös's money.
On the wall of Graham's old office, in Murray Hill, New Jersey, was a sign: "Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who learnt to wear shoes, bathe and not make messes in the house."
Near the sign was the Erdös Room, a closet full of filing cabinets containing copies of more than a thousand of Erdös's articles. "Since he had no home," said Graham, "he depended on me to keep his papers, his mother having done it earlier. He was always asking me to send some of them to one person or another."
Graham also handled all of Erdös's incoming correspondence, which was no small task. Graham had less success influencing Erdös's health. "He badly needed a cataract operation," he said. "I kept trying to persuade him to schedule it. But for years he refused, because he would be laid up for a week and he didn't want to miss even seven days of working with mathematicians."
Like all of Erdös's friends, Graham was concerned about his drug-taking. In 1979, Graham bet Erdös $500 that he couldn't stop taking amphetamines for a month. Erdös accepted the challenge and went cold turkey for 30 days. After Graham paid up - and wrote the $500 off as a business expense - Erdös said: "You've showed me I'm not an addict. But I didn't get any work done. I'd get up in the morning and stare at a blank piece of paper. I'd have no ideas, just like an ordinary person. You've set mathematics back a month." He promptly resumed taking pills.
In 1987, Graham built an addition to his house in Watchung, New Jersey, so that Erdös would have his own bedroom, bathroom and library for the month or so he was there each year. Erdös liked staying with Graham because the household contained a second strong mathematician, Graham's wife, Pam Chung, a Taiwanese émigré who is a professor at the University of Pennsylvania. When Graham wouldn't play with him, Chung would and the two co-authored 13 papers, the first in 1979.
Back in the early 1950s, Erdös started spurring on his collaborators by putting out contracts on problems he wasn't able to solve. By 1987, the outstanding rewards totalled about $15,000 and ranged from $10 to $3,000, reflecting his judgment of the problems' difficulty.
Now that he has gone, Graham and Chung have decided to pay the cash prizes themselves for Erdös's problems in graph theory.
Graham and Erdös would seem an unlikely pair. Although Graham is one of the world's leading mathematicians, he did not, like Erdös, forsake body for mind. Indeed, he continues to push both to the limit. At 6ft 2in with blond hair, blue eyes and chiseled features, Graham looks at least a decade younger than his 62 years. He can juggle six balls and is a former president of the International Jugglers' Association. He is an accomplished trampolinist, who put himself through college as a circus acrobat.
In the middle of solving mathematical problems, he will spring into a handstand, grab stray objects and juggle them, or jump up and down on the super-springy pogo stick he keeps in his office. "You can do mathematics anywhere," said Graham. "I once had a flash of insight into a stubborn problem in the middle of a back somersault with a triple twist on my trampoline."
Erdös and Graham met in 1963 in Boulder, Colorado, at a conference on number theory and immediately began collaborating, writing 27 papers and one book together. That meeting was also the first of many spirited athletic encounters the two men had.
"I remember thinking when we met that he was kind of an old guy," said Graham, "and I was amazed that he beat me at Ping-Pong. That defeat got me to take up the game seriously." Graham bought a machine that served Ping-Pong balls at very high speeds.
Even when Erdös was in his eighties, they still played occasionally. "I'd give him 19 points and play sitting down," said Graham. "But his eyesight was so bad that I could just lob the ball high into the air and he'd lose track of it."
In later years, Erdös came up with novel athletic contests at which he would seem to have more of a chance, although he invariably lost. "Paul liked to imagine situations," said Graham. "For example, he wondered whether I could climb stairs twice as fast as he could. We decided to see. I ran a stopwatch as we both raced up 20 flights in an Atlanta hotel.
"When he got to the top, huffing, I punched the stopwatch but accidentally erased the times. I told him we'd have to do it again. 'We're not doing it again,' he growled and stormed off.
"Another time, in Newark airport, Erdös asked me how hard it was to go up a down escalator. I told him it could be done and I demonstrated. 'That was harder than I thought,' I said. 'That looks easy,' he said. 'I'm, sure you couldn't do it,' I said. 'That's ridiculous,' he said. 'Of course I can.'
"Erdös took about four steps up the escalator and then fell over on his stomach and slid down to the bottom. People were staring at him. He was wearing this ratty coat and looked like he was a wino from the Bowery. He was indignant afterward. 'I got dizzy,' he said."
Erdös and Graham were like an old married couple, happy as clams but bickering incessantly, following scripts they knew by heart, although they were baffling to outsiders. Many of these scripts centred on food. When Erdös was feeling well, he got up at about 5am and started banging around. He would like Graham to make him breakfast, but Graham thought he should make his own. Erdös loved grapefruit and Graham stocked the refrigerator when he knew Erdös was coming.
On a visit in the spring of 1987, Erdös as always peeked into the refrigerator and saw the fruit. In fact, each knew that the other knew that the fruit was there. "Do you have any grapefruit?" asked Erdös.
"I don't know," replied Graham. "Did you look?"
"I don't know where to look."
"How about the refrigerator?"
"Where in the refrigerator?"
"Well, just look."
Erdös found a grapefruit. He looked at it and looked at it, and got a butter knife. "It can't be by chance," explained Graham, "that he so often used the dull side of the knife, trying to force his way through. It'll be squirting like mad, all over himself and the kitchen. I'd say, 'Paul, don't you think you should use a sharper knife?' He'd say, 'It doesn't matter', as the juice shoots across the room. At that point, I'd give up and cut it for him."
In mathematics, Erdös's style was one of intense curiosity, a style he brought to everything else he confronted. Part of his mathematical success stemmed from his willingness to ask fundamental questions, to ponder critically things that others had taken for granted.
He also asked basic questions outside mathematics, but he never remembered the answers. He would point to a bowl of rice and ask what it was and how was it cooked. Graham would pretend he didn't know; others at the table would patiently tell Erdös about rice. But a meal or two later, Erdös would be served rice again, act as though he had never seen it and ask the same questions.
Erdös's curiosity about food, like his approach to so many things, was merely theoretical. He never actually tried to cook rice. In fact, he never cooked anything at all, or even boiled water for tea. "I can make excellent cold cereal," he said, "and I could probably boil an egg, but I've never tried." He was 21 when he buttered his first piece of bread, his mother or a domestic servant having always done it for him.
"I remember clearly," he said. "I had just gone to England to study. It was teatime and bread was served. I was too embarrassed to admit that I had never buttered it. I tried. It wasn't so hard."
But outside mathematics, Erdös's inquisitiveness was limited to necessities, such as eating and drinking; he had no time for frivolities such as sex, art, fiction or movies. Erdös last read a novel in the 1940s, and it was in the 1950s that he apparently saw his last movie, Cold Days, the story of an atrocity in Novi Sad, Yugoslavia, in which Hungarians brutally drowned several thousand Jews and Russians.
Once in a while, the mathematicians he stayed with forced him to join their families on non-mathematical outings, but he accompanied them only in body. "I took him to the Johnson Space Center to see rockets," recalled one of his colleagues, "but he didn't even look up."
Melvyn Nathanson, whose wife was a curator at the Museum of Modern Art in New York, dragged Erdös there. "We showed him Matisse," said Nathanson, "but he would have nothing to do with it. After a few minutes, we ended up sitting in the Sculpture Garden doing mathematics."
When Paul Erdös died, on September 20, 1996, he left an epitaph for himself: Vegre nem butulok tovabb ("Finally I am becoming stupider no more").
Documentary about him:
_________________ "He saw towers and walls in nighted depths under the sea, and vortices of space where wisps of black mist floated before thin shimmerings of cold purple haze. - H. P Lovecraft "The Haunter of the Dark".
"There has been no genetic change since we were hunter-gatherers, but deep in the mind of modern man is a simple hunter-gatherer rule: strive to acquire power and use it to lure women who will bear heirs; strive to acquire wealth and use it to buy affairs with other men’s wives who will bear bastards . . . Wealth and power are means to women; women are means to genetic eternity.
Likewise, deep in the mind of modern woman is the same hunter-gatherer calculator, too recently evolved to have changed much: strive to acquire a provider husband who will invest food and care in your children; strive to find a lover who can give those children first-class genes. Only if she is very lucky will they both be the same man . . . Men are to be exploited as providers of parental care, wealth and genes." - Matt Ridley "The Red Queen"
"Humor won’t save you; it doesn’t really do anything at all. You can look at life ironically for years, maybe decades; there are people who seem to go through most of their lives seeing the funny side, but in the end, life always breaks your heart. Doesn’t matter how brave you are, how reserved, or how much you’ve developed a sense of humor, you still end up with your heart broken. That’s when you stop laughing. In the end there’s just the cold, the silence and the loneliness. In the end, there’s only death." - Houellebecq
Joined: 28 Aug 2011, 17:55 Posts: 2359
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I fear you obsess for the wrong things. Like my friend who used to operate on himself, break his own legs to see if he could put them back. Until a teacher enlightened him on the untimely death of a like minded fellow. Its unhealthy.
Joined: 04 Aug 2009, 19:07 Posts: 5119
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Y'know...I actually have heard of this guy. I was doing really badly in high school geometry (I was never good at math, but I sucked a big one at geometry), but I could get extra credit if I wrote a paper on a mathematician. I chose this guy, and the teacher was even telling me how he met him once.
Why any of this matters...I do not know.
_________________ "The only thing necessary for the triumph of evil is for good men to do nothing."
Joined: 07 May 2012, 05:54 Posts: 28 Location: USA
3 times in 3 posts
this is an interesting thread. I'm not surprised about Erdos, though. It seems to me like the only people men can impress with their intelligence are other men. Women don't really care about it at all.
_________________ "I could have been wild, and I could have been free, but nature played this trick on me..."
Joined: 24 Mar 2012, 00:24 Posts: 395
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The thing is I read things like this and I think how I wouldn't be using technology if these people hadn't come along and discovered theorums that made their creation possible. Where would we be without them? No computers, no LS forum. Population smaller. There is more consciousness because of them because there are more living brains. A good thing or not, only the Supreme Fascist knows..
When you solve for one set of problems previously unsolvable you have the means to arrive at the next set of problems currently unsolvable. I think L.S is the current unsolvable that yesterday couldn't even be dreampt of as extant. And that love is not so much an extant from the bygone but something that even now can be barely imagined.
Joined: 20 Jun 2012, 21:53 Posts: 37 Location: London
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It takes a special level of arrogance as well as ignorance to actually live like that. This guy was so stimulated from the inside he didn't even notice what was going on around him. Savant really.
Eh...I would just say that living inside your head can become addictive.
Living inside my head is what I have done far too much of.
Paul Erdős had a life that looks like a nightmare to me.
I want to relate to other people, to have a wife and family and to live in a community - and to live in the world rather than an abstract world constructed by my imagination and some difficult, dry papers that few people can even read.
Nothing against mathematicians - I've just had a lack of adventure and actual time spent living my life. Too busy with exams and intellectual things.
Joined: 16 Aug 2009, 08:55 Posts: 3119 Location: El Paso, TX, USA
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It takes a special level of arrogance as well as ignorance to actually live like that. This guy was so stimulated from the inside he didn't even notice what was going on around him. Savant really.
You don't understand the world that Erdos came from. Erdos was part of my parents' social circle. That circle was the intellectual Hungarian Jews. In Hungary, before WW2, there was a Jewish culture that was extremely intellectual and where intellectual accomplishment got the kind of respect that becoming a billionaire or a rock star has in America. In that environment, someone who focused on mathematics wasn't socially isolated at all, rather the opposite. This culture produced numerous famous mathematicians and physicists. I realize all this is completely alien to Americans.
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