# Paul Erdös

# Paul Erdös

**1913-1996**

**Hungarian Mathematician**

Paul Erdös was widely assumed by his colleagues to be one of the most brilliant, and perhaps most eccentric, mathematicians of the twentieth century. Erdös established the field of discrete mathematics, which set the stage for the emergence of computer science. Although Erdös studied varied fields of mathematics, it was number theory that occupied him most of his life. He was widely known for posing simply stated mathematical problems that required complex solutions involving the relationships between numbers—then simplifying the complex solutions his colleagues had labored to deliver.

Erdös was born in Budapest, Hungary, to a mother and father who were both mathematics teachers. His genius presented itself early when, at three years of age, Erdös multiplied three-digit numbers in his head, and found negative numbers for himself when he subtracted 250 degrees from 100 degrees—arriving at the solution of 150 degrees below zero. Erdös briefly attended public school as a child, though left due to his mother's fear that the schools were germ-laden (Erdös's two sisters had died of scarlet fever). She preferred that her son learn at home with the help of a governess.

When Erdös reached age 17, his mother allowed him to attend the University of Budapest, where he earned a doctorate degree in mathematics within four years. Erdös completed postdoctoral study in Manchester, England, in the late 1930s. Afterwards, fleeing the persecution of Jews in Hungary, Erdös moved to the United States. Erdös did not affiliate solely with any one university or institution. Instead, he began a life of travel, owning few personal possessions and focusing his efforts on the research and exchange of his mathematical ideas.

By the age 20, Erdös made his first major contribution to number theory, a simpler and more elegant proof of a theorem regarding prime numbers proved previously by Russian mathematician Pafnuty Chebyshev (1821-1894). The theorem states that for every prime number greater than one, there always exists at least one more prime number between it and its double.

In 1949 Erdös and Norwegian mathematician Atle Selberg (1917- ) found an elementary proof of the Prime Number Theorem, which involves the patterns of prime number distribution. Though a joint effort, Selberg published his research first and won the Fields Medal in 1950 for his contribution to this milestone in mathematics. Characteristically indifferent to the politics of academics, Erdös remained unaffected by the oversight. Throughout his life he donated most of the funds he earned from major prizes—including the Cole Prize of the American Mathematical Society in 1961 and the Wolf Prize in 1983—to colleagues or institutions of mathematics. In fact, Erdös often created his own awards, paying as much as $1,000 to students or colleagues who were able to solve problems set up by Erdös.

Erdös was one of the most prolific mathematicians in history, authoring more than 1,000 articles. Fellow mathematicians who co-authored works with Erdös were so numerous that the concept of the "Erdös Number" became popular conversation among the world mathematics community. Erdös numbers describe the number of collaborative efforts with Erdös himself, or those who have a published Erdös collaboration in common. In fact, Erdös's collaborations were so numerous that articles stemming from research partnered before his death continue to be published today.

To foster these partnerships and gain inspiration, Erdös spent little time in one place. A lifelong bachelor, he shuffled from one professional conference to another at universities and research institutions throughout the world. Erdös accepted the hospitality of his colleagues who housed him, fed him, and performed many of the everyday tasks of living, such as filing his taxes and arranging for dental appointments and travel. In return, Erdös would often announce to his host, "My brain is open," and thereby begin to shower his host with the latest mathematical topics and challenges. Then, with his half-packed suitcase, Erdös departed for the next engagement. During one such meeting, a mathematics conference in Warsaw, Poland, Erdös suffered a heart attack while working on an equation, and died at the age of 83.

**BRENDA WILMOTH LERNER**

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**Paul Erdös**