Paul Erdos

Paul Erdős, born Pál Erdős (IPA: ˈɛrdøːʃ ; Budapest, March 26, 1913-Warsaw, September 20, 1996), was an immensely prolific and famous for his eccentricity Hungarian mathematician who, with hundreds of collaborators, worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability.

His life was documented in the film N is a Number: The Portrait of Paul Erdős, made while he was still alive, and the book The Man Who Only Loved Numbers (1998).

He died of a heart attack on September 20, 1996, at the age of 83, while attending a conference in Warsaw, Poland.

Biography

Childhood

Paul Erdős was born in Budapest (Austro-Hungarian Empire), on March 26, 1913, into a family of Jewish origin (the original family name was Engländer). His parents, Anna and Lajos Erdős, had two daughters, aged between three and five, who died of scarlet fever just days before Paul was born. Naturally, this had the effect of Lajos and Anna being extremely protective of Paul. At the age of 3 he already knew how to add and by 4 he could calculate how many seconds a person had lived. Little Paul was as passionate about mathematics as his parents, both mathematicians and teachers of said science.

Paul was just over a year old when the First World War broke out. Lajos, his father, was captured by the Russian army when they attacked the Austro-Hungarian troops. He spent six years in captivity in Siberia. While Lajos was away from the family, Paul's mother, Anna, worked as a teacher during the day. Anna, overly protective after the loss of her two daughters, kept Paul away from school for much of his early years and provided him with a tutor to teach him in her home.

After the First Great War, Miklós Horthy, a right-wing nationalist, assumed control of the country. Her mother was removed from her position as school principal fearing for her life and that of her son, as Horthy's men roamed the streets killing communists and Jews. In 1920, Horthy had introduced laws against Jews similar to those that Hitler would introduce in Germany thirteen years later. That same year, his father, Lajos, returned home from her captivity in Siberia.

Youth and exile

In the interwar era, as Erdős grew older, hostility towards the Jews increased. Erdős knew from an early age that one day he would have to leave Hungary. When he was only six years old, faced with the rise of anti-Semitism, he suggested a conversion. "You can do whatever you want," said the boy, "but I'm going to continue being the way I was born."

Despite restrictions on Jews entering Hungarian universities, Erdös, as winner of a national examination, was allowed to enter in 1930. He studied for his doctorate at the Pázmány Péter University in Budapest.

He obtained his doctorate in 1934, at the age of 21, and left Hungary to settle in Manchester, England, due to the resurgence of fascism in his country of origin. During his stay in England, Erdős traveled extensively throughout the United Kingdom. He met Hardy in Cambridge in 1934, and Stanisław Ulam, also in Cambridge, in 1935. His friendship with Ulam was important to introduce to Erdős later, when he was in the United States.

The situation in Hungary in the late 1930s clearly made it impossible for anyone of Jewish origins to return. However he visited Budapest three times a year during his stay in Manchester. In March 1938 Hitler took control of Austria through the Anschluss and Erdös had to cancel his intention to visit Budapest during the spring. He made the visit during the summer holidays, but the Czech crisis of September 3, 1938 made him decide to hastily return to England. A few weeks later Erdős would travel to the US, where he took up a scholarship at Princeton University.

His life in the United States and McCarthyism

In 1938 he moved to the United States, where he would spend the next ten years. Then, as he once recalled, “my problems started with Joe and Sam.” That same year he accepted his first position at Princeton University. Around this time, he began to develop the habit of traveling from one campus to another, visiting mathematicians, a habit he would retain until his death.

Although he wanted to see his mother again—his father had died of a heart attack and much of his family had been murdered in the Holocaust—he did not want to return to Hungary because of " Joe" (Joseph Stalin, in English Joseph). In 1954, however, he was invited to a mathematics conference in Amsterdam. As a foreigner, he would have to apply for a return visa to the United States, usually a matter of routine. But his extensive correspondence with mathematicians outside the United States, and especially with a mathematician in Communist China, raised the suspicion of immigration officials during the era of McCarthyism. He was a member of the mathematics department at the University of Notre Dame.

"Immigration officials asked me all kinds of stupid questions," Erdős recalled. They asked him about Marx. He had only read the Communist Manifesto and responded: "I am not competent to judge, but he was undoubtedly a great man." As a result, his visa was denied. Forced to choose between the safety of his members, the University of Notre Dame and the freedom to travel, he did not hesitate. He attended the conference and spent most of the next decade in the State of Israel. His applications for a visitor visa to attend conferences in the United States were repeatedly rejected. In 1958 the State Department granted him a "special visa" to attend a conference in Colorado. During his stay, an immigration official accompanied him everywhere. In 1962 he wrote to his friends that apparently "US foreign policy consists of two points: the non-admission of Red China to the UN and the non-admission of Paul Erdős to the US.".

Material possessions were of no importance to Erdős; Prizes and other profits were usually donated to people in need or as rewards for solving problems that he himself proposed. He spent most of his life as a vagabond, traveling between scientific conferences and the homes of fellow mathematicians around the world. Typically, he would arrive at the door of the house where he was a guest and say, "My brain is open," staying long enough to craft a few articles before traveling again. On several occasions, he would ask his host who he should pay his next visit to. His working style has been humorously compared to a linked list.

As his colleague Alfréd Rényi said: "a mathematician is a machine that turns coffee into theorems", and Erdős drank large quantities. (This quote is continually attributed to Erdős, but it seems that Rényi was actually the first to use it.)

He also had his own vocabulary: he spoke of The Book, an imaginary book in which God had written the most beautiful proofs of mathematical theorems. In a 1985 lecture he commented: "You don't have to believe in God, but you should believe in The Book." He himself doubted the existence of God, whom he called the "Supreme Fascist", and whom he accused of keeping the most elegant proofs unshared. When he found some particularly beautiful mathematical proof, he would exclaim "This is one for The Book!"

Other elements of his particular vocabulary were: "epsilons" to refer to children; women were "chiefs" and men were "slaves"; the people who had stopped working in mathematics were "dead" and those who had died were "gone"; alcoholic beverages, "poison"; music, "noise"; When he taught a class, he "preached." For his epitaph she suggested something like "I finally stopped becoming stupid" (Hungarian: "Végre nem butulok tovább").

He died "in action" of a heart attack on September 20, 1996, at the age of 83, while attending a conference in Warsaw (Poland). He never married or left children.

Professional work

Erdős was one of the most prolific publishers of mathematical articles of all time, surpassed only by Leonhard Euler (Erdős published more articles, but Euler published more pages). He wrote approximately 1,500 articles in his lifetime, collaborating with around 500 co-authors. He firmly believed in mathematics as a social activity.

Among his contributions, contributions to Ramsey's theory and the application of the probabilistic method stand out.

Erdős number

Due to his numerous contributions, collaborators and friends invented the Erdős number as a tribute with overtones of mathematical humor: Erdős is assigned the number 0, all those who collaborated on an article with him have 1, someone who has collaborated with one of his collaborators has 2, and so on... Simple estimates prove that 90% of mathematicians assets have an Erdős number less than 8 (it seems surprising if one does not know the theory of Six Degrees of Separation).