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:

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.

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.

Sounds like a very large child.

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.

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.

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.

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.

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.