Atle Selberg, one of the last of the 20th century's great mathematicians, who had "a golden touch" in expanding on the work of his predecessors, died of a heart attack Aug. 6 at his home in Princeton, N.J. He was 90.

Los Angeles Times
OBITUARIES
By Thomas H. Maugh II
August 22, 2007

Selberg, a prolific researcher in a variety of fields during his six-decade career, will long be remembered through the mathematical terms that now bear his name: the Selberg trace formula, the Selberg sieve, the Selberg integral, the Selberg class, the Rankin-Selberg L-function, the Selberg eigenvalue conjecture and the Selberg zeta function.

"His far-reaching contributions have left a profound imprint on the world of mathematics, and we have lost not only a mathematical giant but a dear friend," said Peter Goddard, director of the Institute for Advanced Study at Princeton University, where Selberg spent most of his career.

Said mathematician Peter Sarnak of Princeton, "The 20th century was blessed with a number of very talented mathematicians, and of those, there are a few I would say had a golden touch. In any topic about which they thought in depth, they saw further and uncovered much more -- seemingly effortlessly -- than the generations before them. Their work set the stage for many future developments. Atle was one such mathematician; he was a mathematician's mathematician."

Selberg burst onto the international scene in 1949 with his simple and elegant proof of the so-called prime number theorem, which describes the distribution of prime numbers in the universe of whole numbers. Prime numbers are those that can be evenly divided only by themselves and by one -- such as three, seven and 11.

The prime number theorem was formulated in the 18th century and had been proved in 1896 by Belgian and French mathematicians.

Their proof was viewed as one of the greatest achievements of analytic number theory, but it required the use of difficult complex functions.

Selberg and mathematician Paul Erdos independently proved the theorem without using complex function theory, a breakthrough that startled the mathematical community.

They were originally scheduled to publish their papers back to back in a mathematical journal, but for reasons that have never been made fully clear, Selberg decided to publish his paper earlier in a different journal and he received the bulk of the credit for the achievement.

In large part because of this proof, he was awarded the 1950 Fields Medal for young mathematicians -- an award frequently considered the Nobel Prize for mathematicians.

Selberg then turned his attention to the even more esoteric theories of automorphic forms, which relate the geometry of certain types of surfaces to the frequencies at which they can vibrate.

In a 1956 paper in the Journal of the Indian Mathematical Society, he introduced what came to be known as the Selberg trace formula, which led to the discovery of unexpected connections between the properties of prime numbers and those of geometric surfaces.

"This is one of the most influential mathematical papers of the 20th century," Sarnak said. "It lays the foundations and many of the tools on which the modern theory of automorphic forms, with its many spectacular applications, rests."

[Click here for the rest of the article on-line.]