ALL HARMONIZES

Prime Obsession: Will the greatest problem in mathematics ever be resolved? (Margaret Wertheim, 8/22/03, LA Weekly)

With a pedigree linking many of the greatest names in the field, the Riemann Hypothesis runs like a river through vast swaths of seemingly distinct mathematical territory. Andrew Wiles himself has compared a proof of this proposition to what it meant for the 18th century when a solution to the longitude problem was found. With longitude licked, explorers could navigate freely around the physical world; so too, if Riemann is resolved, mathematicians will be able to navigate more fluidly across their domain. Its import extends into areas as diverse as number theory, geometry, logic, probability theory and even quantum physics.

The Riemann Hypothesis is a proposal about prime numbers, the atomic elements of the number system. Primeness is one of the most essential concepts in mathematics, for primes - 2, 3, 5, 7, 11 and so on - are numbers that cannot be broken into any smaller elements. All other integers can be built up by multiplication of these basic units. So, for example, 6 is built up from 2 x 3, 15 from 3 x 5, 49 from 7 x 7. In his book The Riemann Hypothesis, science writer Karl Sabbagh makes an analogy between numbers and molecules. All of the vast plethora of molecules that inhabit our world, everything from salt and ammonia to hemoglobin, are made up of the basic elements of the periodic table - carbon, hydrogen, oxygen and so on. As Sabbagh notes, the primes may be seen as the periodic table of the number system. Yet where the elements follow a clear pattern, the primes seem to be distributed randomly.

To mathematicians, randomness is anathema. As du Sautoy writes, they "can't bear to admit that there might not be an explanation for the way nature has picked the primes." That would be like "listening to white noise"; what mathematicians crave above all else is harmony. They want, they need, they demand a pattern behind the apparent chaos. Du Sautoy quotes the great French mathematician and physicist Henri Poincare: "The scientist does not study nature because it is useful, he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and if nature were not worth knowing, life would not be worth living."

For many mathematicians life would not be worth living if the organization of the primes did not ultimately conform to some beautiful underlying order. The Riemann Hypothesis proposes what that order might be.

We're down with the French dude on this one. Posted by Orrin Judd at August 21, 2003 11:24 PM