We have all heard of unusual geniuses in art and music, even in science sometimes. But there are extraordinary individuals in every creative field. It is not easy for everyone to understand, let alone appreciate, the work and value of their contributions to human thought and culture.
In the field of mathematics, for example, there have been quite a few exceptionally gifted people, and some of them lived rather unusual lives, bordering on the eccentric. As in music, some of the marvelous capacities of the human spirit are expressed through such geniuses.
Paul Erdös (born: 26 March 1913) was one of them. He born in Hungary and of Jewish parents, but he never felt strong affiliation to any region or religion, seeing himself only as a human being. He had no interest in politics or pettiness of any sort. He had equal contempt for communism and capitalism and their major spokes-nations of the 20th century. He derisively referred to the U.S. as Samland (Uncle Sam’s country) and the Soviet Union as Joedom (the realm of Joseph Stalin).
His highly technical output is far too esoteric to be translated into everyday language. He received some of the highest awards and prizes conferred on the practitioners of the profession, like the Cole Prize and a letter of appreciation from the Fields Medal Committee. Because had passed the age of forty he was not eligible for the medal which he richl;y deserved otherwise.
Though some of these came with a hefty check, Erdös cared little for money. He gave it away to poor students or as prize money. He himself lived a very sparse life. Like religious ascetics, he never married.
But there is at least one major accomplishment of Erdös that must be intelligible to many people. All we need to know is that a prime number N is one which cannot be written as the product of different numbers (other than as 1 x N). Now consider the number 4 and its double 8. Between these two there are two primes 5 and 7. Or consider 15 and its double 30. Between them we have the primes 17, 19, 13, and 29. In the 19th century it was known conjectured (the Bertrand Postulate) that between any number x and its double 2x, there are is always at least one prime, as illustrated above. In the 20th century some eminent mathematicians proved it, but the proof was complicated. At 19, Erdös gave an elegant proof for this result in number theory. He also proved (without invoking complex numbers) the so called prime number theorem which gives an estimate with an upper limit for the number of primes there are below a stipulated number.
Since he was interested in little else aside from mathematics, all of Erdös’s intellectual energies were devoted to mathematics. His primary interest was in number theory. But he was also a major architect of what is called discrete mathematics which is of enormous import in computer science. He collaborated (wrote joint papers) with at least 462 mathematicians: more than anyone else had done. He authored more than 1500 papers during his lifetime. More were published posthumously.
Erdös had a pungent wit. As an atheist who had suffered under fascist regimes, he described God as a Supreme Fascist. He referred to children as epsilons (small entities in the mathematical jargon). He did not care for marriage, referring to women as bosses and to men as slaves in the context. He suggested the following for his epitaph: Végre nem butulok tovább (Finally I am becoming stupider no more).
Paul Hoffman’s The Man Who Loved Only Numbers is an enjoyable biography of this genius. Epic poets, composers of magnificent music, great painters and mathematicians: They all function in higher realms where they create or harvest rich fruits and share them with the rest of us, if we are sophisticated enough to be able to relish them.
March 26, 2011