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.

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."

For The Record

Los Angeles Times Saturday, August 25, 2007 Home Edition Main News Part Page News Desk 1 inches; 43 words Type of Material: Correction

Selberg obituary: The obituary of mathematician Atle Selberg in Wednesday's California section said the Institute for Advanced Study was located at Princeton University. The institute, which was founded in 1930, is in Princeton, N.J., but it has never been affiliated with the university.

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."

Atle (pronounced AHT-luh) Selberg was born June 14, 1917, in Langesund, Norway.

His father, Ole, was also a mathematician and the younger Selberg was exposed to mathematical books at an early age.

One of his first memorable experiences occurred at the age of 13, when he encountered the formula for determining the value of pi divided by 4: (pi)/4 = 1 - 1/3 + 1/5 - 1/7. . . .

Selberg later described it as "such a very strange and beautiful relationship that I determined I would read that book in order to find out how this formula came about."

He later encountered the collected works of Indian mathematician Srinivasa Ramanujan, which an older brother had brought home from school. Stimulated by the book, at age 17 he wrote his first paper, "On Some Mathematical Identities."

After entering college at the University of Oslo, Selberg submitted the paper to one of his professors and it was published a year later.

He had published 11 papers by the time he received his doctorate from Oslo in 1943. Most of them remained obscure for several years, however, because of World War II.

Selberg defended his doctoral thesis in November 1943, just before Nazi occupiers closed down the university for the duration of the war.

He spent five years as a research fellow at the University of Oslo before marrying Hedvig Liebermann of Tirgu Mures, Transylvania, and moving to the United States in 1947. After short stints at the Institute for Advanced Study and at Syracuse University in New York, Selberg became a full-time staff member at the institute and remained there for the rest of his career.

After his formal retirement, he traveled widely, attending math camps and experimental workshops with the goal of promoting math among young people.

In addition to the Fields Medal, Selberg received the Wolf Prize in mathematics in 1986.

In 1989 and 1991, his journal articles were reprinted in a two-volume collection that made many of them -- which had been published originally in Norwegian or in journals of limited distribution -- widely available for the first time.

Hedvig Selberg died in 1995 and Selberg subsequently married Betty Compton of Princeton. In addition to his wife, he is survived by a daughter, Ingrid Maria Selberg of London; a son, Lars Atle Selberg of Middlefield, Conn.; stepdaughters Heidi Faith of Mountain View, Calif., and Cindy Faith of Roland Park, Md.; and four grandchildren.

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thomas.maugh@latimes.com