Pál Erdös (1913 - 1996)

Pál (Paul) Erdös, one of the most extraordinary men of our times, died in Warsaw on the 20th of September 1996.

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.

Tomasz Luczak