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Professor sees magic, mystery in mathematics

  1. April 27, 2007
  2. Rick DelVecchio, Chronicle Staff Writer
  3. SAN FRANCISCO CHRONICLE
  4. http://sfgate.com/cgi-bin/article.cgi?f=/c/a/2007/04/27/BAGS7PGB2N1.DTL&type=science

Marcus du Sautoy takes the stage in Berkeley today hoping to light up his audience with the story of how thrilling it is to be a mathematician.

The Oxford professor and writer says there's nothing quite like the rush of doing pure math, the foundation of the universe. As he describes it, math is an activity far closer to the exhilaration of performing live theater than slogging through arithmetic in a classroom.

People "rear back," as he puts it, when they learn what he does for a living. Little do they know the fun he's having as he pits himself against some of the world's greatest unsolved mysteries -- notably the mystery of prime numbers -- and associates with composers, choreographers and sculptors. Mathematicians have much in common with artists, he believes. They're all looking for patterns that say something universal. Math, no less than art, is about beauty and symmetry.

"Mathematics I really love because of its creative side," said an animated du Sautoy, a trumpeter and soccer player on the side, during a phone interview with The Chronicle. "If not this, I would have run away to a theater company."

Du Sautoy's talk -- it's free in Room 2050 of the Valley Life Sciences Building on the UC Berkeley campus and starts at 5:15 p.m. -- centers on his book, "The Music of the Primes."

The book traces humankind's quest -- from the ancient Greeks to today's amateur sleuths armed with powerful computers -- to uncloak the patterns behind the randomness of those numbers which can be divided only by themselves and 1 -- 2, 3, 5, 7, 11, 13, 17, 19, 23 ... . The primes.

The primes stretch from 2 to infinity and "are the very atoms of arithmetic,'' he writes in his book. "Look through a list of prime numbers, and you'll find that it's impossible to predict when the next prime will appear. The list seems chaotic, random and offers no clues as to how to determine the next number."

Modern calculating power keeps finding larger and larger primes, the most enormous stretching to nearly 10 million digits and spelled shorthand in the form of 2 to the 32,582,657th power -1, according to the Web site primes.utm.edu/largest.html.

But do all these feats of calculation bring us any closer to solving the mystery? Not particularly. Because solving the mystery, it seems, requires an Einsteinian, right-brain creative leap. The answer has to be visualized, not figured out.

There are clues. In 1859, the German mathematician Bernhard Riemann uncovered a possible pattern in the distribution of primes. He didn't solve the mystery but pointed later generations of mathematicians in a most promising direction.

In the 1940s, Nobel Prize- winning physicist Eugene Wigner noticed that the spectral lines of heavy atoms were governed by an unusual probability distribution.

Then, in 1996, Peter Sarnak and Zeev Rudnick found that a related distribution applied to primes, suggesting a deeper underlying similarity to physics.

"The harmonics of the primes were distributed in the same patterns as the spectral lines of heavy metals -- very suggestive idea," said UC Berkeley math Professor David Eisenbud, director of the Berkeley-based Mathematical Sciences Research Institute, which is hosting today's event. "Who would imagine that the spectral lines of heavy atoms were related to prime numbers?"

The question is open. But the hint is that primes are not abstract, not mere playthings.

"One can start to read really mystical things into this," du Sautoy said. "It can almost give you a spiritual buzz to feel these connections, but you mustn't take it too far."

One of the math heroes profiled in du Sautoy's book is David Hilbert, who used to chalk formulas on a 20-foot blackboard in his garden in Konigsberg and had such an intense belief in the abstract power of math that physical objects were irrelevant to him, du Sautoy writes. Hilbert posed 23 problems for mathematicians to work on in the 20th century, of which the mystery of primes is the major one to remain untoppled.

"There are at least 20 different approaches," said Brian Conrey, executive director of the American Institute of Mathematics in Palo Alto. "I can't say seriously at this time somebody has the right idea. We're still struggling, definitely."

When will primes give up their secrets? "The word on the street," Eisenbud said, "is we might see it in my lifetime."

Du Sautoy talks about primes as if they can be appreciated by the math-averse as a part of nature. For example, he says cicadas emerge on a 17-year cycle and suggests they hit on a prime as an evolutionary strategy to keep predators guessing. He says that when someone catches a ball the brain is automatically performing high-level math.

The soccer star David Beckham wears No. 23 for Real Madrid. For Manchester United, his number was 7. Significant? Du Sautoy thinks so.

When Beckham moves to the Los Angeles Galaxy this summer, is he going to wear another prime? "I'm hoping for a really big one, like 71," the mathematician said.

Du Sautoy plays amateur soccer and believes the reason his team advanced one year was because everyone wore a prime number. However, the theory suffered a blow when the team later got demoted, du Sautoy said.

After his talk today, du Sautoy will go home to England to be with his family before flying to Syria, China and India to film a BBC series on the history of math.

Du Sautoy says more people around the world are catching the thrill of math. He points to movies and TV shows and puzzles like Sudoku.

"It's really a rush of adrenalin," he said. "Mathematics is one great, grand Sudoku. It's really a drug."

E-mail Rick DelVecchio at rdelvecchio@sfchronicle.com.

This article appeared on page B - 2 of the San Francisco Chronicle