Sunday, July 22, 2007

The Riemann Hypothesis, mathematics community, and automatons

During the past several years, I have grown fascinated by the Riemann Hypothesis. The real mathematics of the problem makes my eyes glaze over even though I have an undergraduate degree in mathematics. People have published several popular expositions on the problem over the past several years; I have read four of them. That helps in getting the gist of the work on the problem before and after Riemann. The Internet has good resources on the problem also.

I wonder why my fascination with the problem has not burned itself out. For one, the mathematics community makes it easy for me to explore the problem to any depth I want. I view the mathematics community as a wonderful computer at my disposal. The great mathematicians of the past and present create new mathematics and publish it. With the Riemann Hypothesis, the worlds most famous and important unsolved math problem, many people act as interpreters of the mathematics and publish the interpretations. I ask the computer to show me a paper, or I buy a book with the real mathematics in it. I read it. Something interests me. I ask the computer to find me someone who has interpreted the mathematics in terms of what I can understand. The computer spits out several articles or books by interpreters; I read the articles on the Internet or study the books.

In essence, for me, the mathematics community is an automaton at my disposal. I can enjoy contemplating a problem such as the Riemann Hypothesis without ever having to do any work except study the work others have done on the problem.

The Riemann Hypothesis is about how many primes are less than a given number. Now that is a problem deceptively, even viciously, easy to understand. After that, things turn difficult in a hurry. Yet I enjoy trying to prove certain results on my own. That goes nowhere, yet I get the sense of just how difficult the problem is. I appreciate more the work of mathematicians.

The same might be the case with art. I cannot paint, but I could try to copy a painting I like just to see how difficult it is to produce that painting. The community of artists is an automaton also. I punch a button, out comes something I like.

Anyway, I need to punch some more buttons on my mathematics community automaton. I enjoy it. Maybe, more patterns and connections will form in my mind.

Like it or not, we all use each other as automatons more than we care to admit.