Paul Erdős ( ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician known as one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered on discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics.
He taught at various universities in the United States and Israel. Erdős's output was prolific; he published around 1,500 mathematical papers during his lifetime, many being collaborations with other mathematicians, making him arguably the most prolific mathematician in history. This prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships.
He was known both for his social practice of mathematics, working with more than 500 collaborators, and for his eccentric lifestyle. He firmly believed mathematics to be a social activity, living a nomadic lifestyle with the sole purpose of writing mathematical papers with other mathematicians. He devoted his waking hours to mathematics, even into his later years; he died at a mathematics conference in Warsaw in 1996.
Early life and education
Paul Erdős was born on 26 March 1913, in Budapest, Austria-Hungary, the only surviving child of Anna (née Wilhelm) and Lajos Erdős (né Engländer). His parents, both Jewish, were high school mathematics teachers. His fascination with mathematics developed early. He was raised partly by a German governess causing his mother to have to work long hours to support their household. His father had taught himself English while in captivity but mispronounced many words. When Lajos later taught his son to speak English, Paul learned his father's pronunciation, which he continued to use for the rest of his life.
He taught himself to read through mathematics texts that his parents left around in their home. By the age of five, given a person's age, he could calculate in his head how many seconds they had lived. Due to his sisters' deaths, he had a close relationship with his mother, with the two of them reportedly sharing the same bed until he left for college.
When he was 16, his father introduced him to two subjects that would become lifetime favourites—infinite series and set theory. In high school, Erdős became an ardent solver of the problems that appeared each month in KöMaL, the "Mathematical and Physical Journal for Secondary Schools".
Erdős began studying at the University of Budapest when he was 17 after winning a national examination. At the time, admission of Jews to Hungarian universities was severely restricted under the numerus clausus.
During 1933, Erdős and several other students, including George Szekeres, Esther Klein (later Szekeres), her lifelong friend Márta Wachsberger (later Svéd), and George Svéd, met frequently, often at the Anonymous statue in City Park, about which Szekeres and Erdős wrote a paper that generalised the result in 1935. Erdős dubbed the original problem the "Happy ending problem" because it resulted in the marriage of George and Esther Szekeres.
By the time he was 20, Erdős had found a proof for Bertrand's postulate. Time magazine called him "The Oddball's Oddball". Except for some years in the 1950s, when he was not allowed to enter the United States based on the accusation that he was a Communist sympathizer, his life was a continuous series of going from one meeting or seminar to another.
In 1943, Erdős began a part-time appointment at Purdue University. In the same year, Stanisław Ulam invited Erdős to work on the Manhattan Project in Los Alamos, New Mexico, with him, along with other mathematicians and physicists. However, Erdős expressed a desire to return to Hungary after the war. in 1954, the United States Immigration and Naturalization Service denied Erdős, a Hungarian citizen, a re-entry visa into the United States. The official reasons were the fact that he had corresponded with a Chinese mathematician who had subsequently returned from the United States to China, and also Erdős's 1941 FBI record.
In 1985, he visited two universities in Adelaide, South Australia, Flinders University and the University of Adelaide. At the latter, he met budding mathematician Terence Tao, then 10 years old. Erdős reportedly enjoyed working with children. His trip to Australia was instigated by longtime friend and collaborator, Hungarian mathematician George Szekeres.
Mathematical work
Erdős was one of the most prolific mathematician and producer of mathematical conjectures in history, if not the most.