John Derbyshire in “Prime Obsession” introduces the reader to the intriguing world of mathematics.  We all know numbers at the most basic level: it’s how we count, but there is a science to numbers and many theories of viewing numbers in a more scientific way.   Derbyshire focuses on one aspect of numbers: prime numbers.   Prime numbers are numbers that cannot be divided by other numbers and give a whole number as an answer.   Examples are 3, 5, 7, 11, etc.  The occurrence of prime numbers diminishes as the numbers get larger.   Is there some mathematical formula that predicts the occurrence of prime numbers as the numbers get larger?   In 1859, the brilliant thirty-three year old Bernard Riemann, while giving a paper on sequencing numbers, alluded to there being a predictable sequence of prime numbers, but his paper was on a different topic, and he did not elaborate.   No one took notice of his offhand comment until after he died when his true genius was fully appreciated.

Riemann was recognized as an intellectual giant during his lifetime.   He gave many technical papers on Euclidian and non-Euclidian geometry and worked on theoretical descriptions of space.   His work on warped space was picked up by Einstein when Einstein formulated his theory of relativity.   Riemann’s chance remark introduced an enigma that mathematicians have been trying to solve for one hundred and fifty years.   Riemann never published his proof that prime numbers follow a predictable sequence.  Because of Riemann’s stature as a great mathematician, the possibility that he knew the sequence has become a challenge for subsequent mathematicians.   Nobody has discovered any predictability to the occurrence of prime numbers, but many have tried and are still trying.   The advent of computers have simplified the laborious task of dividing large numbers with known prime numbers, and some people have discovered truly enormous numbers that are prime.   Did Riemann really know the sequence but was more interested in his speech at the time?  Nobody knows, and no one, not even the most talented mathematician, has been able to discover what Riemann was alluding to.

Derbyshire makes his book interesting by alternating his chapters between outlining the history of mathematical theories with more technical chapters explaining many of the theories.   He starts with the Greeks and Euclidian geometry and continues in alternate chapters until the present time.   His more technical chapters, however, are not so technical that the average reader cannot understand the explanations.   Although we all know what numbers are, few of us realize what higher math and theoretical considerations can do with numbers.   It’s a good education to read Derbyshire’s book and a fascinating exercise in realizing how to understand numbers better.

Why do numbers have the relationship with each other that they have?   I don’t have the slightest idea.  However, reading “Prime Obsession” was interesting and informative.  It made me realize that there is much more to this universe we live in than meets the eye.   I recommend “Prime Obsession” as a good read.