The wandering mathematician: Paul Erdos
It is well known that many mathematicians are a little eccentric. Their values differ somewhat from the average. Although they are good at counting, they do not highly appreciate money, nor the things money can buy. In this set of eccentrics, perhaps the most eccentric who ever lived was Paul Erdos (1913-1996).
Born in Budapest to two high school mathematics teachers, he was a wunderkind who discovered negative numbers at the age of four. He wrote his first academic paper at the age of 18 and kept on writing papers up to the age of 83, thereby falsifying the theorem that mathematics is a young person’s game.
Indeed, Erdos was probably the most prolific mathematician of the 20th century. He wrote during his lifetime some 1,500 papers in learned periodicals; that works out at about a paper in every three weeks. How did he do it? By working day and night (he was known to need only five hours of sleep) on the one hand, and on the other by having co-authors who were more than happy to do the actual writing. Most people in the scientific world have co-authors (colleagues, research assistants, doctoral students), so that is not surprising. What is surprising is the actual number of co-authors. Erdos had more than five hundred. No other mathematician ever got near to that figure.
How did he operate? He would choose a university with a good mathematics department. “Have you got any unsolved problems?” he asked. “I shall be in your city next Monday. My mind is open. Let us solve those problems together. I have many conjectures too. You are welcome to them.”
This way of finding collaborators in the pursuit of mathematics was highly unconventional. But it worked. It worked because this was the way he chose to live and this led to a vast number of collaborators and to a vast number of papers that made everyone happy. He had no hobbies, no wife, no interest in sex, no fixed abode, no permanent job. So what did he live on? The most reliable source of his income came from fees for lectures he gave. He also received considerable amounts of money in the form of international prizes for the work he had done. Of those the most generous and most prestigious was the Wolf Prize he received in 1983, worth $50,000. He kept only $700 dollars for himself, and donated the rest to worthy causes, not necessarily related to mathematics.
His needs were modest. All his belongings were contained in a small suitcase, sometimes accompanied by a medium-sized plastic bag. He was always ready to move. To be nomadic was obviously an acquired characteristic. He did not inherit that from his parents.
His life as a mathematician started at the age of 21, when he received a doctorate from the University of Pazmany Peter in Budapest. His fame must have quickly reached the British Isles. He was awarded a four-year Fellowship by Manchester University. His wanderlust started at about the same time, by visiting mathematicians in Britain (including G. H. Hardy at Cambridge} and returning each year three times to Budapest.
In 1938 he made the wise decision to move to the United States. Of his extended family who remained in Hungary, only his mother survived. Erdos spent most of the Second World War working in the mathematics departments of Notre Dame and Purdue Universities and in Princeton at the Institute of Advanced Studies where, among others, Einstein and von Neumann worked too. He was offered a position at Notre Dame University, Indiana, after the war. He did not accept it; instead he started his itinerant career. During the McCarthy era he was refused a re-entry visa, as he was suspected of being a Communist sympathiser. He was apparently forgiven in 1963 when the ban was withdrawn and he could return to the United States.
Erdos had few interests outside mathematics. Actually he did have other interests, but just could not spare the time to pursue them. Of human affairs he was rather pessimistic. He was variously described as an agnostic or atheist. He was unlikely to have been one of God’s favourites, referring to him as the Supreme Fascist. Erdos blamed God not so much for allowing mass murder, but for the smaller offence of hiding his glasses and passports.
An excellent description of Erdos’ hectic life-style was given by one of his collaborators, Chip Ordman. It can be found in the biography by Paul Hoffman, The Man Who Loved Only Numbers. Ordman visited Erdos in Budapest in 1988 when he was hospitalised there after a mild heart attack. The room where he stayed was unusually big, to accommodate all the people who wanted to see him. According to Ordman “there were journals piled up and papers everywhere. Erdos was lying there holding three mathematical conversations at once: in Hungarian with a group in one corner, in German with a group in another corner and in English with a third group, all this while talking to me and my wife. The doctors came in and he said: ‘Go away, can’t you see that I am busy? Come back in a few hours.’ And that’s what they did.”
It is not unreasonable for mathematicians to want some numerical measure of some human activity — in this case, how Erdos’s influence spread. The measure concocted by Erdos’ friends is the so-called Erdos number. Those with Erdos number 1 are those who wrote a paper with Erdos. Erdos number 2 are those who wrote a paper jointly with an Erdos number 1, and so on. It can be generalised, saying that an Erdos number n is a mathematician who wrote a paper with an Erdos number n-1.
All people who use their brains after nominal retirement complain that they are losing their marbles, but as far as I know it is only Erdos who thought it worth mentioning this unfortunate fact in his epitaph. It reads in Hungarian: “Vegre, nem butulok tovabb”. In English: “At last I stopped becoming more demented.” In fact, he had little reason to complain. Between the ages of sixty and eighty, Erdos wrote no fewer than fifty papers.
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