Atle Selberg

Atle Selberg, 90, who was known as one of the great mathematicians of the 20th century and was a winner of the Fields Medal, which is often considered the Nobel Prize of mathematics, died Aug. 6 at his home in Princeton, N.J. He had a heart ailment.

Since 1949, Selberg had been associated continuously with the Institute for Advanced Study in Princeton, the former academic home of Albert Einstein and one of the most prestigious of American scholarly institutions.

The institute's director, Peter Goddard, described Selberg as "a mathematical giant" and said in a statement that "his far-reaching contributions have left a profound imprint on the world of mathematics."

Peter Sarnak, a professor at the institute's School of Mathematics, said in the statement released by the institute that Selberg "was a mathematician's mathematician."

Selberg possessed "a golden touch" and prepared the way for many future findings, Sarnak said.

The area in which Selberg specialized was analytic number theory.

In the simplest terms, number theory can be described as the study of the properties of the integers, which include the common numbers employed in daily life.

But modern number theory has reached a level of complexity and abstraction that places full appreciation of its achievements beyond the capacity of all but a few.

"I don't think that other people have had grave difficulties understanding my work," Selberg said in 1990.

In its statement, the institute said he maintained "an understated view" of his accomplishments.

The Fields Medal was awarded to Selberg for his work on proving a challenging theory about the distribution of prime numbers.

For years, mathematicians had believed that it could be proved only by the laborious application of ponderous techniques. In 1949, Selberg and another celebrated mathematician, Paul Erdos, achieved a proof through techniques of startling simplicity.

Each, it was reported, was to report on his own contribution in the same issue of the same mathematics journal.

Because of what has been described as a misunderstanding that led to hurt feelings, Selberg published first.

His Fields Medal, recognizing him for a variety of accomplishments, followed.

Selberg was born June 14, 1917, in Langesund, Norway, the youngest child of a mother who was a teacher and a father who was himself a mathematician.

An equation found in one of his father's books inflamed Selberg's mathematical curiosity at the age of 13.

It showed a way of expressing (pi)/4, in which pi is the celebrated irrational number designating the ratio of the circumference of a circle to its diameter.

Selberg was determined to learn what produced "such a very strange and beautiful relationship."

Later, he said, he was strongly influenced by "remarkable, strange and beautiful" formulas in the works of Srinivasa Ramanujan, the brilliant, largely self-taught Indian-born mathematician who made important contributions to number theory.

In a talk given in India to honor the 100th anniversary of Ramanujan's birth, Selberg noted the difficulties Ramanujan had suffered in an "inflexible and rigid educational system."

This, Selberg said, showed that schools should know when to make exceptions.

At all levels, he said, "allowances should be made for the unusual and perhaps lopsidedly gifted child with very strong interests in one direction."

Selberg's first wife, Hedvig, died in 1995. Survivors include his second wife, Betty Compton Selberg; two children from

his first marriage; two stepdaughters; and four grandchildren.