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May 12, 2000

The solution of a mathematical poser that has baffled experts for 30 years has been hailed as an important breakthrough in number theory.

Researchers have made the discovery concerning Gollnitz theorem, a particularly far-reaching theory in a branch of mathematics called partitions, that may turn out to have practical implications in areas such as statistics and theoretical physics.

The experts - Krishnaswami Alladi, chairman of the University of Florida's department of mathematics, and colleague Alexander Berkovich - are to unveil their findings in a fortnight at the Millennial Conference on Number Theory at the University of Illinois in the United States.

"Without any exaggeration, this is one of the most exciting things that has happened in this subject, and the consequences that will be worked out over the next several years will be quite significant," said Professor Alladi.

The problem the pair has solved was first posed 30 years ago by George Andrews, professor of mathematics at Pennsylvania State University and one of the world's foremost authorities on partitions.

The theory of partitions was founded by Leonard Euler, the famous 18th-century mathematician.

It deals with the representation of numbers as sums of other numbers, something that arises in a host of different settings.

Professor Andrews, who collaborated with the Florida mathematicians on the project, said: "It has been a dream of mine since 1967 that someday I would see an extension of the Gollnitz theorem. I lost hope after 30 years, so this is an especially delicious moment."

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