Paul Erdos

If the Martians had made contact with earth during the lifetime of Paul 
Erdos he would have made a good choice as this planet's ambassador. The 
aliens would have appreciated his unearthly intelligence. He spoke the 
universe's common tongue, the theory of numbers, with fluency and wit. 
Importantly, Mr Erdos would never have missed the trappings of this world. 
He had no children, no wife, no house, no credit card, no job, no change 
of shoes, indeed nothing but a suitcase containing a few cSothes and some 
notebooks. Neither was he fussy about food, as long as he had coffee. 
A mathematician, he said, "is a machine for converting coffee into 
theorems." Mr Erdos's life was streamlined for mathematics.

	Mathematics? For many it is the most baffling of the sciences. 
Most people with a bit of education can follow an explanation of say, the 
Big Bang or genetics, but limit their interest in mathematics to sorting 
out the intricacies of their bank statement. To mathematicians, though, 
their science is the purest creation of the human mind, and for many Mr 
Erdos was its supreme exponent this century.

	Typically, he would arrive in a city where he was to lecture, ring 
up a fellow mathematician, and announce, "My brain is in town." He sounds 
like a guest from hell, but to his hosts this brain was a shared treasure 
and their collective responsibility. They would lodge him, feed him, launder 
his clothing.

	Paul Erdos was a constantly wandering Jew. For much of his life 
Hungary, his homeland, was run by dictators. Many members of his family were 
murdered by the Germans during the Hitler period. In return for the comfort 
of friends who took care of his perfunctory needs, Mr Erdos would cut gems 
of elegance from numbers, graphs and logic. His problems were often simple 
to pose, yet offered room for creativity and surprise. Suppose an infinite 
number of dots are painted on an infinite canvas in such a way that the 
distance in inches between any two dots is a whole number. What would the 
painting look like? Mr Erdos's brow would furrow as he showed that the result 
could only be a straight row of dots. But don't ask for an explanation of 
his elegant proof unless you are interested in conic sections.

	In his prime

Paul Erdos's parents were maths teachers, so they presumably looked at him 
fondly when, at four, he said he had discovered negative numbers. While in 
his late teens he made discoveries about prime numbers. A number is "prime" 
if it cannot be divided by any smaller number except one. Examples of prime 
numbers are 1913, the year in  which Mr Erdos was born, and 83, his age 
when he died of a heart attack at a mathematics conference in Warsaw. 
Mr Erdos helped to recast a theory about I prime numbers made by an earlier 
mathematican, using a more elegant approach. This, it was said, was analogous 
to creating the Panama Canal for shipping that previously went around 
South America.

Elegant indeed, but were Mr Erdos's l,000 or more published papers of any 
practical value?  He made no claim for their practicality. It was enough, 
he said, that a proof was "very nice". Yet mathematics, however pure, has 
a way of turning up in useful places. "Combinatorics", a branch of maths 
explored by Mr Erdos, can be used to calculate the number of tiles needed 
to pave an irregular space. His work on graphs has been applied to the design 
of communications networks.

	The extraordinary left side of his brain was put at the service of 
numerous young mathematicians at the start of their careers. To him a 
mathematician of promise was an epsilon, the Greek letter used by 
mathematicians to describe a small quantity. To an epsilon he was "Uncle 
Paul". He set them problems, paying them rewards of a few hundred dollars 
if they came up with solutions, giving away much of his modest income from 
lectures and prizes (among them the Wolf Prize, an Israel-based sort of 
Nobel prize). A colleague likened Mr Erdos to a honeybee: an industrious 
creature who buzzed about the world and pollinated the fields of mathematics.

	He was compared to Leonhard Euler (1707-83), an awesome Swiss 
regarded as the most prolific mathematician who ever lived. It is hard 
to exaggerate Mr Erdos's passion. For 19 hours a day, seven days a week, 
stimulated by coffee, and later by amphetamines, he worked on mathematics. 
He might start a game of chess, but would probably doze offuntil the 
conversation retumed to maths. To find another life this century as 
intensely devoted to abstraction, one must reach back to Ludwig Wittgenstein 
(1889-1951), who stripped his life bare for philosophy. But whereas 
Wittgenstein discarded his family fortune as a form of self-torture, Mr 
Erdos gave away most of the money he earned because he simply did not 
need it. "Private property is a nuisance," he would say. And where 
Wittgenstein was driven by near suicidal compulsions, Mr Erdos simply 
constructed his life to extract from his magnificent obsession the maximum 
amount of happiness.


Photo caption reads: Paul Erdos, mathematician and eccentric, died
on September 20th, aged 83.

The Economist, October 5th 1996, page 83.