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New York Zeros

06/26/02 12:00AM By Dan Rockmore
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(Host) Commentator Dan Rockmore reflects on those times when nothing is really something - even downright inspiring.

(Rockmore) The other week, lured by the promise of zillions of zeros, my mathematician pals Peter and Laurie boarded the train at White River Junction and met me in New York City.

These weren't the zeros that represent the primacy of New York's numerosity, but rather, these are the zeros that hold the key to understanding the prime numbers, the fundamental building blocks of the natural numbers.

Prime numbers are those numbers that can be divided evenly by only themselves and one. Two is prime, three is prime, five is prime, but six is not prime, since it can be divided by both two and three. Primes are numerical DNA, since any number is uniquely the product of its prime factors.

Since ancient times, we've known that there are infinitely many primes, but it wasn't until relatively recently that mathematicians began to try to understand the rate at which the primes pop up as we count along the number line. Curiously, the farther you go, the rarer they seem to be. In 1859, a German mathematician, Bernard Riemann, discovered something he called the zeta function, which seemed to hold the key to this mystery.

Now the zeta function is a mathematical function; and mathematical functions are kind of like machines that take numbers as their raw material, and apply various transformations like squaring, multiplying and dividing, in order to produce a new number. Riemann's zeta function is a very complicated function and the great surprise is that we would have a very precise knowledge of the frequency of prime numbers, if only we could know which initial inputs cause Riemann's zeta function to produce a zero. These zero-producing inputs are the zeta zeros and one hundred and fifty years after Riemann, the person who uncovers the secret to the zeta zeros will add a bunch of zeros to his or her bank account by winning a one million dollar prize, courtesy of England's Clay Institute of Mathematics.

Laurie and Peter had come to New York so that we could all attend a math conference devoted to the zeta zeros in downtown New York, at New York University's Courant Institute of Mathematical Sciences.

Ironically, just one day later, New York was the site of yet another zero-centric meeting, this one just a short jog south of our own gathering. In a somber ceremony at Ground Zero, New York's newest and saddest tourist attraction, the city and nation marked the end of the recovery work and the start of a renewal of public spirit and effort.

We've got a huge and daunting task ahead, but as I looked around the conference hall at our international crew of mathematicians, representing a spectrum of religious, national and ethnic identities, ignorant of difference, bound by a shared interest in the pursuit of knowledge and the understanding of a universal truth, I felt a glimmer of hope. At least we aren't starting from nothing.

From Hanover New Hampshire, this is Dan Rockmore.

Dan Rockmore is a professor of mathematics and computer science at Dartmouth College.
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