## Pál Erdös (1913 - 1996)
Pál (Paul) Erdös, one of the most extraordinary men of our times,
died in Warsaw on the 20
There is hardly a mathematician who never came into contact with
this wise man, full of serene distance towards himself and the
world around him. He used to spend his time in incessant travels,
rarely staying more than two weeks at one place. He carried all
his belongings with him: a half-empty suitcase and a briefcase
with the papers he was currently working upon. Even if he possessed
almost nothing else, every one who was in need could count on
his aid. After lecturing in India he sent his remuneration for
the lectures to the widow of Srivanas Ramanujan (a self-taught
mathematician of exceptional talent), whom, incidentally, he never
met. When awarded the very prestigious and one of the most lucrative
mathematical prizes, the Wolf Prize, in 1984, he immediately founded
a scholarship that bore his mother's name. He also detected several
people who, in his opinion, needed that money much more than he
did, and eventually he was left with slightly more than $700 out
of a prize of $50,000. Needless to say, this fact did not bother
him in the least. Thinking of material goods was always considered
by him a loss of time.
His real passion was mathematics and in particular, solving and
formulating problems. His brilliant and extremely effective approach
to the questions he was working on became legendary: quite often
he was able to provide an astounding solution of a problem from
an area almost completely unknown to him, using only general information
provided to him by a patient companion at a dinner table. This
ability of his bordered on magic, no wonder then that already
in the thirties he was given the nickname of "the magician
of Budapest". Above all, however, he was an unequalled master
in posing questions, almost always significant and deep, although
in most cases formulated in a very elementary way. In spite of
their diversity, the problems he tackled surprisingly composed
an astonishing and harmonious image. Colleagues even used to say
that they are all particular conclusions derived from the one
and unique great mathematical metatheory held in his mind, of
the existence of which he may have been unconscious himself.
He treated the results of his considerations just as he treated
material goods, offering them generously to others, always eager
to tell about the questions that attracted his interest, exhaustively
presenting all the successful and unsuccessful intents to solve
them and the partial results obtained. If there was a problem
that would not succumb to his piercing attacks, he assigned a
reward, with the sense of humour that was so specific of him,
ranging from $5 to $3000. It is not surprising then that many
of the papers bearing his name were co-authored by one, and sometimes
two or more mathematicians, unknown to each other, each of whom
contributed to the solution of the problem with his own part.
With time this cooperation reached so important a dimension, that
mathematicians began to assign to each other the so-called Erdös
number. Co-authors of papers written with Erdös were assigned
Erdös number one, co-authors of papers written together with Erdös's
co-authors were assigned the number two, co-authors of co-authors
of co-authors had Erdös number three, and so on. By the time of
Erdös's death there were over 500 co-authors of his papers, a
phenomenon never registered in the history of mathematics, and
about 5,000 mathematicians with Erdös number two.
Erdös's attitude towards mathematics and mathematicians was well
reflected by the language he described his world with, full of
warm irony and terms taken from mathematics, philosophy and theology.
Two notions bore special significance in this peculiar dialect.
The first was the "Book", the place where the simplest
and at the same time the most penetrating proofs of mathematical
theorems were gathered. A proof "straight from the Book"
meant an argument close to perfection. When presented with a complicated
reasoning that shed little light on the essence of the question,
Erdös felt worried: "This is true, but it might be worthwhile
to find a proof straight from the Book." The second term,
equally important in his life, was "epsilon", the name
he used to give to a young person interested in mathematics. Erdös
gave particular significance to his contacts with the epsilons.
He took solicitous care of young mathematicians and secondary
school pupils, urging them to go into research and, still more
important, assailing them with problems he considered to be within
their reach. In this area he was very successful indeed: numerous
ex-epsilons became eminent mathematicians and the Hungarian school
of combinatorics is second to none.
It might seem that in today's world of highly specialized science
an eminent scientist is expected to avoid unnecessary distraction
of mind and to concentrate on one particular question, to construct,
alone or with a group of collaborators, a theory that would allow
to understand, clarify or prove a phenomenon, a regularity or
a theorem. Examples of such an approach abound. Let's just mention
the physicists in their attempts (unsuccessful till now) to conceive
a unifying theory for all the four known kinds of interaction,
or Andrew Wiles, whose long years of solitary work resulted in
a proof of Fermat's Last Theorem. The life of Pál Erdös proves
that this is not the only possible way. Never did he attempt to
construct monumental theories (although his works had contributed
to the emergence of many). He left over 1400 papers, more than
anyone before him, on problems which attracted him just because
they were interesting. He was one of the few who used to recall
that both in science and in life not only the power and correctness
of an argument count, but its depth and beauty as well. |