# Atle Selberg

# Atle Selberg

**1917-**

**Norwegian-American Mathematician**

In 1950, Atle Selberg received the Fields Medal for his generalizations of Viggo Brun's sieve methods, and for a proof relating to the Riemann zeta function. He is also noted for a proof of the prime number theorem, on which he worked with Paul Erdös (1913-1996).

Born on June 14, 1917, in Langeslund, Norway, Selberg was the son of Ole and Anna Skeie Selberg. Inspired by reading about the Indian mathematical prodigy Ramanujan as a child, he decided on a career in mathematics, and was further inspired by a lecture he heard at the International Mathematical Conference in Oslo in 1936. He performed his doctoral studies at the University of Oslo, where he earned his degree in 1943. A year earlier he had been appointed a resident fellow of the university, and would remain in that position for five years.

In 1947, Selberg emigrated to the United States. Also in 1947, he married Hedvig Liebermann, with whom he later had two children, Ingrid and Lars. He spent his first year in America at the Institute for Advanced Study at Princeton, then taught for a year as associate professor of mathematics at Syracuse University before returning to the Institute as a permanent member in 1949.

During this period, Selberg did much of his most important work, a great deal of it in the area of generalizing the findings of others. Thus he generalized the number-sieve methods of Viggo Brunn, a study that was linked to his investigations in the Riemann zeta function. With regard to the latter, Selberg was able to prove that a positive proportion of the zeroes in the zeta function satisfy the Riemann hypothesis concerning them.

Also during this time, Selberg and Erdös both attacked the proof of the prime number theorem, a problem of long standing that Bernhard Riemann (1826-1866) himself had tried unsuccessfully to complete. The theorem had actually been proven, independently and simultaneously, in 1896 by Jacques Hadamard (1865-1963) and Charles de la Vallée-Poussin (1866-1962). However, they had used complex analysis, whereas Selberg and Erdös were able to provide an elementary proof that required no complex function theory. For reasons that are unclear, Selberg published his findings before Erdös, and received most of the credit for the proof.

After receiving the Fields Medal in 1950, Selberg became a professor at Princeton. Among his other awards were the Wolf Prize in 1986, and an honorary commission of Knight Commander with Star from the Norwegian Order of St. Olav in 1987. In later years, Selberg has traveled extensively, participated in commemorative events, and taken an interest in mathematics education among high-schoolers.

**JUDSON KNIGHT**

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**Atle Selberg**