The TIMES

September 25 1996
# PAUL ERDOS

Paul Erdos, mathematician, died on September 20 aged 83. He was born
on March 26, 1913.
Paul Erdos was regarded by fellow mathematicians as the most
brilliant, if eccentric, mind in his field. Because he had no interest
in anything but numbers, his name was not well known outside the
mathematical fraternity. He wrote no best-selling books, and showed a
stoic disregard for worldly success and personal comfort, living out
of a suitcase for much of his adult life. The money he made from
prizes he gave away to fellow mathematicians whom he considered to be
needier than himself. "Property is a nuisance," was his succinct
evaluation.
Mathematics was his life and his only interest from earliest childhood
onwards. He became the most prolific mathematician of his generation,
writing or co-authoring 1,000 papers and still publishing one a week
in his seventies. His research spanned many areas, but it was in
number theory that he was considered a genius. He set problems that
were often easy to state, but extremely tricky to solve and which
involved the relationships between numbers. He liked to say that if
one could think of a problem in mathematics that was unsolved and more
than 100 years old, it was probably a problem in number theory.
In spite, or perhaps because of, his eccentricities, mathematicians
revered him and found him inspiring to work with. He was regarded as
the wit of the mathematical world, the one man capable of coming up
with a short, clever solution to a problem on which others had
laboured through pages of equations. He collaborated with so many
mathematicians that the phenomenon of the "Erdos number" evolved. To
have an Erdos number 1, a mathematician must have published a paper
with Erdos. To have a number of 2, he or she must have published with
someone who had published with Erdos, and so on. Four and a half
thousand mathematicians have an Erdos number of 2.
Erdos was born into a Hungarian-Jewish family in Budapest, the only
surviving child of two mathematics teachers (his two sisters, who died
of scarlet fever, were considered even brighter than he was). At the
age of three he was amusing guests by multiplying three-digit numbers
in his head, and he discovered negative numbers for himself the same
year. When his father was captured in a Russian offensive against the
Austro-Hungarian armies and sent to Siberia for six years, his mother
removed him from school, which she was convinced was full of germs,
and decided to teach him herself. Erdos received his doctorate in
mathematics from the University of Budapest, then in 1934 came to
Manchester on a post-doctoral fellowship.
By the time he finished there in the late 1930s it was obvious that it
would be an act of suicide for a Jew to return to Hungary. Instead
Erdos left for the United States. Most members of his family who
remained in Hungary were killed during the war.
Erdos had made his first significant contribution to number theory
when he was 20, and discovered an elegant proof for the theorem which
states that for each number greater than 1, there is always at least
one prime number between it and its double. The Russian mathematician
Chebyshev had proved this in the 19th century, but Erdos's proof was
far neater. News of his success was passed around Hungarian
mathematicians, accompanied by a rhyme: "Chebyshev said it, and I say
it again/There is always a prime between n and 2n."
In 1949 he and Atle Selberg astounded the mathematics world with an
elementary proof of the Prime Number Theorem, which had explained the
pattern of distribution of prime numbers since 1896. Selberg and Erdos
agreed to publish their work in back-to-back papers in the same
journal, explaining the work each had done and sharing the credit. But
at the last minute Selberg (who, it was said, had overheard himself
being slighted by colleagues) raced ahead with his proof and published
first. The following year Selberg won the Fields Medal for his
work. Erdos was not much concerned with the competitive aspect of
mathematics and was philosophical about the episode.
From 1954 Erdos began to have problems with the American and Soviet
authorities. He was invited to a conference in Amsterdam but on the
way back into the United States was interrogated by immigration
officials over his Soviet sympathies. Asked what he thought of Marx,
he gave a typically guileless response: "I'm not competent to judge,
but no doubt he was a great man." Denied his re-entry visa, Erdos left
and spent much of the 1950s in Israel.
He was allowed back into the United States in the 1960s, and from 1964
his mother, now in her mid-eighties, began travelling with him. Apart
from his family and old friends, Erdos had no interest in a
relationship which was not founded in shared intellectual curiosity
and he was content to remain a bachelor.
Nor did he see the need to restrict himself to one university. He
needed no equipment for his work, no library or laboratory. Instead he
criss-crossed America and Europe from one university and research
centre to the next, inspired by making new contacts. When he arrived
in a new town he would present himself on the doorstep of the local
most prominent mathematician and announce: "My brain is open."
He would work furiously for a few days and then move on, once he had
exhausted the ideas or patience of his host (he was quite capable of
falling asleep at the dinner table if the conversation was not
mathematics). He would end sessions with: "We'll continue tomorrow P
if I live." After the death of his mother in 1971, Erdos threw himself
into his work with even greater vigour, regularly putting in a 19-hour
day. He fuelled his efforts almost entirely by coffee, caffeine
tablets and Benzedrine. He looked more frail, gaunt and unkempt than
ever, and often wore his pyjama top as a shirt. Somehow his body
seemed to thrive on this punishing routine.
Because of his simple lifestyle, Erdos had little need of money. He
won the Wolf Prize in 1983, the most lucrative award for
mathematicians, but kept only $720 of the $50,000 he had
received. Lecturing fees also went to worthy causes. The only time he
required funds was when another mathematician solved a problem which
Erdos had set but not been able to solve. From 1954 he had spurred
his colleagues on by handing out rewards of up to $1,000 for these
problems.
He died from a heart attack at a conference in Warsaw, while he was
working on another equation.