Erdos 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 around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studied 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.

Erdos entered the University of Budapest at the age of 17. By the time he was 20, he had found a proof for Chebyshev's Theorem. Erdos later published several articles in the monthly about problems in elementary plane geometry. In 1934, at the age of 21, he was awarded a doctorate in mathematics. Erdos's thesis advisor was Lipƒt Fejùr, who was also the thesis advisor for John von Neumann, George Pƒlya, and Paul (Pñl) Turñn. Because he was a Jew, Erdos decided Hungary was dangerous and relocated to the United States. Many members of Erdos' family, including two of his aunts, two of his uncles, and his father, died in Budapest during the Holocaust. His mother survived in hiding. He was living in America and working at the Princeton Institute for Advanced Study at the time.

Possessions meant little to Erdos; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were generally donated to people in need and various worthy causes. He spent most of his life traveling between scientific conferences, universities and the homes of colleagues all over the world. He earned enough in stipends from universities as a guest lecturer, and from various mathematical awards, to fund his travels and basic needs; money left over he used to fund cash prizes for proofs of "Erdos problems" (see below). 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. In many cases, he would ask the current collaborator about whom to visit next.

In 1954, the United States Citizenship and Immigration Services denied Erdos, a Hungarian citizen, a re-entry visa into the United States, for reasons that have never been fully explained. Teaching at the University of Notre Dame at the time, Erdos could have chosen to remain in the country. Instead, he packed up and left, albeit requesting reconsideration from the U.S. Immigration Services at periodic intervals.

Erdos was one of the most prolific publishers of papers in mathematical history, comparable only with Leonhard Euler; Erdos published more papers, mostly in collaboration with other mathematicians, while Euler published more pages, mostly by himself. Erdos wrote around 1,525 mathematical articles in his lifetime, mostly with co-authors. He strongly believed in and practiced mathematics as a social activity, having 511 different collaborators in his lifetime.