A legendary mathematical genius, Paul Erdős was unquestionably the most prolific and eccentric mind of his generation. He has to his name more papers and mathematical conjectures than any other contemporary of the 20th century. Most of his published papers revolved around prime numbers, combinatorics, discrete mathematics, and engaged more than 500 collaborations in problem solving. His greatest contribution was to the Ramsey Theory, a field of combinatorics that studies conditions necessary for order to appear. He fell under the category of a problem solver, who was opposed to a theoretician in the taxonomy of Mathematics, and spent his life solving conjectures. A nomad living out of his suitcase, and a couple of plastic bags, he was famous for arriving at fellow mathematicians’ homes and place of work and declaring that his ‘mind was now open’. Paul Erdős is fondly remembered for his many aphorisms, one of them being SF or Supreme Fascist, which was his denotation for God. He was persecuted throughout his life, and yet he never let go of his humanity, sense of humour, compassion for the less fortunate, or his zeal for mathematics until his last breath.
Childhood & Early Life
Paul Erdős was born on 26th March 1913 to two high school mathematics teachers of Jewish faith, Anna and Lajos Erdős in the Austro-Hungarian city of Budapest.
He had two older sisters, aged 3 and 5 who died from contracting scarlet fever, around the time of his birth. As a result, he did not get to attend school until the age of ten, given his mother’s understandable yet irrational fear of her only surviving child contracting some fatal childhood disease.
His father was captured by Russian troops during World War I and spent roughly six years in a Siberian prisoner of war camp, leaving his mother as the sole provider for the household.
He enrolled into the university in 1930 and simultaneously received his PhD and undergraduate degree in mathematics from University of Budapest in 1934.
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In 1932, he published his first paper which was a proof for Bertrand’s postulate that between any number and its double, there exists one or more prime numbers. While proofs for the same were provided by Chebyshev in 1852 and later in 1919 by Ramanujan, his was by far the most elementary and elegant.
As anti-Semitism intensified in his country, he moved out of Budapest to England where he pursued a four-year post-doctoral fellowship from the University of Manchester from 1934 to 1938. There, he travelled extensively across UK, giving lectures and co-authoring mathematical papers with other likeminded academics.
In 1935, he collaborated with Szekeres to produce a precise proof for one of the many corollaries from Ramsey’s theorem, called the Erdős-Szekeres theorem. That same year, he met Esther Klein, another mathematician and co-authored a paper on the ‘Happy Ending theorem’. He named it so because that collaboration also led to the marriage between Esther and Szekeres.
By September 1938, he realised Europe had become unsafe for him and accepted a scholarship at the Institute for Advanced Studies in Princeton, USA for a period of one and a half years. During that time, he got to mingle with many European refugee scientists like John von Neumann and Albert Einstein.
Over the next decade, he travelled to different universities across America giving guest lectures. During one such visit, his brief encounter with fellow mathematician, Atle Selberg led to the elementary proof for the Prime Number theorem in July 1948. The discovery was marred in controversy as there was dispute over who solved it first.
As the Cold War began in 1950, the US suspected him to be a communist whereas Hungary suspected him to be an American spy, so neither country let him in. At that point, Israel welcomed him to stay, as did Holland and some other countries. Thus, began his circuit of cross continent lectures spanning more than 15 countries.
He was finally allowed to enter the US in late 1963, and that same year, he met Ronald Graham at a Colorado conference on number theory. The two became good friends and co-authored 28 papers together. Graham even built a spare room in his house for Erdős.
He continued with his nomadic lifestyle until his death in 1996, touring the world upon invitation by mathematicians and universities alike, and solved problems for and with them. On the side, he also received exorbitant day rates of $25,000 in some cases from private research entities like IBM, Bell Labs, etc for solving their analytical problems.
As a mathematician, he was famous for his elegant proofs to problems in the field of combinatorics and number theory.
So prolific were his collaborations (close to 500) that it prompted the conceptualization of the ‘Erdős Number’, which is a measure of ‘collaborative distance’ between a mathematician and Erdős in terms of co-authorship.
Awards & Achievements
In recognition of his many papers that he published on number theory, the American Mathematical Society awarded him the Cole Prize in 1951. Three decades later, he received the Wolf Prize in Israel in 1984.
Between 1986 and 1996, he received roughly 15 honorary doctorates and was made honorary member of scientific academies of eight countries.
Family & Personal Life
Having given his life to the pursuit of mathematics, he had no time for romantic relationships or marriage for that matter.
He was extremely close to his mother, who joined him in 1948, and followed him everywhere he went until her death in 1971. His addiction to amphetamines were a direct result of his failure of coping with her death.
Compassionate and principled, he generously donated any monetary proceeds towards worthy causes or to people in need. He kept very little for himself. He also used the money to fund cash prize for proofs to his many mathematical conjectures.
He died aged 83, on September 20th, 1996 in Warsaw, Poland, while attending a conference there. The cause of death was a heart attack.