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Erdős, Pál

(1913–1996), mathematician. Born in Budapest to parents who taught mathematics and physics at the high-school level, Pál Erdős became interested in mathematics and showed exceptional talent at an early age. In college, he belonged to a group of students, most of them Jews, who became lifelong friends, all renowned mathematicians, such as Tibor Gallai (Grünwald), György Szekeres, Géza Grünwald, and Pál Turán. Their talents were stimulated and nurtured by their superior education; they were also decisively influenced by the Hungarian mathematical monthly Középiskolai Matematikai Lapok (Mathematical Journal for Secondary Schools), which was dedicated to problem-solving.

After finishing his university studies, Erdős spent some years in Manchester. Alarmed by the advance of Nazism in Europe, he left Hungary in September 1938 for Princeton, New Jersey, where he held a fellowship at the Institute for Advanced Studies. He returned to Hungary for one short visit before the Communist regime closed the borders in 1949.

From the mid-1950s Erdős traveled with a special Hungarian passport; his official documents declared him to be a Hungarian citizen and an Israeli resident. Although he visited Israel regularly, he rarely spent more than a few weeks there. A true cosmopolitan and a globetrotter, this singular privilege enabled him to travel freely and to maintain a powerful channel of communication between the Hungarian and the international mathematical communities in the era of iron curtain isolation. He showed moral independence and took uncompromising stances toward organizations and even states, supported by his exceptional standing in international mathematics and his freedom from the personal responsibilities of owning property or having a wife and family. Due to his extensive personal and professional connections with mathematicians from Communist countries (connections he neither could nor wanted to conceal from American immigration authorities), Erdős was denied entrance to the United States from 1954 to 1963, except for one brief visit in 1958. In 1973, when Israeli mathematicians were not permitted to participate in a conference organized to celebrate Erdős’s sixtieth birthday, he refused to visit Hungary for three years. At about the same time he refrained from visiting Israel because he was denied a visa that would have enabled him easy entrance to the country.

Erdős was the most prolific mathematician of the twentieth century: he wrote some 1,500 papers (with more than 450 coauthors). Endowed with an extraordinary memory and exceptional skills for communicating mathematics verbally, he exerted a great influence on the development of mathematics in a wide variety of fields, including number theory, analysis, probability theory, graph theory, and set theory. A famous Hungarian school of combinatorics emerged largely under his influence. He received numerous honorary doctorates and prizes, among them the Wolf Prize (in Israel), widely regarded as the equivalent of the Nobel Prize in mathematics.

Erdős’s peripatetic lifestyle, unique worldview, vocabulary, wit, and benevolent deeds made him a legend in his own lifetime; some of the anecdotes about him that appear in popular biographies are not entirely free from journalistic distortions. He died while participating in a Warsaw conference and is buried in a Jewish cemetery in Budapest.

Suggested Reading

László Babai, “In and Out of Hungary: Paul Erdős, His Friends and Times,” in Combinatorics, Paul Erdős Is Eighty, eds. Dezső Miklós, Vera T. Sós and Tamás Szőnyi, vol. 2, pp. 7–95 (Budapest, 1996); Ronald L. Graham and Jaroslav Nešetřil, eds., The Mathematics of Paul Erdős (Berlin, 1997); Gábor Halász, László Lovász, Miklós Simonovits, and Vera T. Sós, eds., Paul Erdős and His Mathematics (Budapest and Berlin, 2002).