The gathering is a culmination of a four-year, $1 million grant--a rare sum for a mathematics award. Gonek and his team received the award to investigate one of the most important unsolved problems in the field. The team focused on a 150-year-old conundrum that is considered the Holy Grail of pure math: the Riemann Zeta Function. The function has tantalized and troubled mathematicians with its promise of revealing the hidden truths of prime numbers.
"Prime numbers hold a very special place in mathematics," says Gonek. "You can think of them as the atoms of the world of numbers. That's why the Riemann
hypothesis is so important--so much of the rest of pure mathematics is built upon the properties of prime numbers, so understanding them can give us incredible insights into how all math functions."
A prime number is only divisible by 1 and itself. The first few are 2, 3, 5, 7, 11, 13, and so on. In 300 B.C., ancient Greek mathematicians proved that there are infinitely many prime numbers. They are important because they are the fundamental building blocks of numbers, just as atoms are the building blocks of molecules: Every number is a unique combination of primes multiplied together. For example, 4 is 2 times 2, and 24 is 2 times 2 times 2 times 3. The great question: Is there any regularity to the occurrence of prime numbers among the other numbers? The Riemann hypothesis implies that the primes are as irregular, or random, as they could possibly be, but this remains an unproven hypothesis.
"In recent years there has been an exciting cross-fertilization between the area of pure number theory that studies the zeta function and a branch of applied mathematics called random matrix theory," says Gonek. "Random matrix theory has been used by physicists for half a century to model the behavior of complicated systems such as heavy nuclei. It was therefore a great surprise when scientists in the two fields realized that tools from each could lead to important insights and surprising advances in the other."
In the early nineties, Gonek, designed and ran a math camp for bright mathematics majors from various colleges, and introduced the workshop idea into math courses at Rochester. He helped design a number of the College's "Quest" courses, including teaching an interdisciplinary Quest course, called "The Infinite," with a colleague from the department of Religion and Classics. In 1998, Gonek won a Goergen Award for Distinguished Achievement and Artistry in Undergraduate Teaching.
Maintained by Office of Communications
Math scholars tackle prime mystery
Gonek
ore than 100 mathematicians from around the world are puzzling over some of the field's most intriguing problems this week in Rochester at a conference titled "Advances in Number Theory and Random Matrix Theory." The event was preceded by a five-day series of workshops at the University co-organized by Steve Gonek, chair of the mathematics department. Sponsored by the University, the American Institute of Mathematics, and the National Science Foundation, the conference bridges theoretical and applied math, combining number theory, the purest form of mathematical study, and random matrix theory, a branch of mathematics used heavily by physicists.
Please send your comments and suggestions to:
Office of Communications.
