Atle Selberg

Atle Selberg (1917–2007) was a Norwegian mathematician whose work shaped analytic number theory, including an elementary proof of the prime number theorem and the Selberg trace formula.

Elementary proof of the prime number theorem: A proof that the number of primes up to a bound follows the prime number theorem without using complex analysis. Selberg and Paul Erdős produced the first such proof using an identity relating sums over primes and integers.
Selberg symmetry formula: An identity relating sums over prime powers to sums over integers through the von Mangoldt function. Selberg used this formula as the central arithmetic step in his elementary proof of the prime number theorem.
University of Oslo: A public research university in Norway, founded in 1811 as the Royal Frederick University. Selberg studied mathematics there before moving into an international research career.
Carl Ludwig Siegel: A German mathematician whose work included number theory, Diophantine approximation, and the theory of automorphic forms. Siegel was a senior colleague at the Institute for Advanced Study during Selberg’s career there.
Fields Medal: An international mathematics award presented every four years to up to four mathematicians under age 40. Selberg received the 1950 medal for contributions including sieve methods and work on the prime number theorem.
Selberg trace formula: A formula relating the spectrum of a Laplacian on a quotient space to geometric data from its closed geodesics. Selberg developed this formula, linking his work to the spectral theory of automorphic forms.
Von Mangoldt function: An arithmetic function equal to the logarithm of a prime on prime powers and zero otherwise. It weights prime powers in the sums appearing in Selberg’s symmetry formula.
Norwegian Academy of Science and Letters: A Norwegian learned society that promotes research and scholarship across academic fields. Selberg’s early recognition in Norway included election to this academy.
André Weil: A French mathematician who made influential contributions to number theory, algebraic geometry, and the history of mathematics. Weil and Selberg were leading figures in the postwar development of modern number theory.
Abel Prize: An international mathematics prize awarded annually by the Norwegian Academy of Science and Letters. Selberg received the 2002 Abel Prize for his work in analytic number theory and discrete groups.

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