Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics.

He was raised partly by a German governess[12] because his father was held captive in Siberia as an Austro-Hungarian prisoner of war during 1914–1920,[10] causing his mother to have to work long hours to support their household.

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.

[12] 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.

[17] Many members of Erdős's family, including two of his aunts, two of his uncles, and his father, died in Budapest during World War II.

[17][18] However, his fellowship at Princeton only got extended by 6 months rather than the expected year due to Erdős not conforming to the standards of the place; they found him "uncouth and unconventional".

[13] Described by his biographer, Paul Hoffman, as "probably the most eccentric mathematician in the world," Erdős spent most of his adult life living out of a suitcase.

[19] 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.

[19] During his visits, Erdős expected his hosts to lodge him, feed him, and do his laundry, along with anything else he needed, as well as arrange for him to get to his next destination.

[19] Ulam left his post at the University of Wisconsin–Madison in 1943 to work on the Manhattan Project in Los Alamos, New Mexico with other mathematicians and physicists.

He once said, I want to be giving a lecture, finishing up an important proof on the blackboard, when someone in the audience shouts out, 'What about the general case?'.

[22] Erdős's name contains the Hungarian letter "ő" ("o" with double acute accent), but is often incorrectly written as Erdos or Erdös either "by mistake or out of typographical necessity".

In 1938, he accepted his first American position as a scholarship holder at the Institute for Advanced Study, Princeton, New Jersey, for the next ten years.

As a result of the Red Scare and McCarthyism,[25][26][27] in 1954, the Immigration and Naturalization Service denied Erdős, a Hungarian citizen, a re-entry visa into the United States.

In 1963, the U.S. Immigration Service granted Erdős a visa, and he resumed teaching at and traveling to American institutions.

[31] Shortly before his death, he renounced his honorary degree from the University of Waterloo over what he considered to be unfair treatment of colleague Adrian Bondy.

Joel Spencer states that "his place in the 20th-century mathematical pantheon is a matter of some controversy because he resolutely concentrated on particular theorems and conjectures throughout his illustrious career.

Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory.

However, the circumstances leading up to the proofs, as well as publication disagreements, led to a bitter dispute between Erdős and Selberg.

[49][needs update] British mathematician Thomas Bloom started a website dedicated to Erdős's problems in 2024.

Due to collaborations with mathematicians, many scientists in fields such as physics, engineering, biology, and economics also have Erdős numbers.

He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later.

[75][76] He playfully nicknamed him the SF (for "Supreme Fascist"), accusing him of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself.

Other idiosyncratic elements of Erdős's vocabulary include:[71] He gave nicknames to many countries, examples being: the U.S. was "samland" (after Uncle Sam)[71] and the Soviet Union was "joedom" (after Joseph Stalin).

"[78] Erdős is the subject of at least three books: two biographies (Hoffman's The Man Who Loved Only Numbers and Schechter's My Brain is Open, both published in 1998) and a 2013 children's picture book by Deborah Heiligman (The Boy Who Loved Math: The Improbable Life of Paul Erdős).

[81] He is also the subject of George Csicsery's biographical documentary film N is a Number: A Portrait of Paul Erdős,[82] made while he was still alive.

In 2021 the minor planet (asteroid) 405571 (temporarily designated 2005 QE87) was formally named "Erdőspál" to commemorate Erdős, with the citation describing him as "a Hungarian mathematician, much of whose work centered around discrete mathematics.

His work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics.