Prime Obsession

Since we’re on the subject of mathematics, let me post a short review of an excellent book, the aforementioned Prime Obsession. It’s written by John Derbyshire, a conservative commentator at National Review Online who trained as a mathematician, and I read it mostly watching the sun rise off the coast of Puerto Rico. While I don’t always agree with the Derb’s positions on politics (and almost never when it comes to religion), the man has produced a very readable, highly enjoyable book for non-mathematicians.

Prime Obsession is subtitled "Bernhard Riemann and the Greatest Unsolved Problem in Mathematics." The book’s got a twist I like: the odd-numbered chapters introduce us to the math behind the unproved Riemann Hypothesis, gently and vividly, and the even-numbered ones bring this poor brilliant man’s history and times to life. What a refreshing change of pace! I enjoy history, and always like to research the history of any topic I’m interested in. Derbyshire really did a good job, here, and I looked forward to the switching of gears that the alternating chapters provided.

So what is the Greatest Unsolved Problem in Mathematics? Simply put, it has to do with a rule or formula for calculating how many prime numbers there are in a given sample of numbers. How many primes are there less than a hundred? A million? A billion? Is there a way to know the answer to these questions without actually having to count and test each and every number in a sample? A clue was first formulated in a paper Riemann wrote in 1859, in which he made a guess (known as the Riemann Hypothesis). The proof of this guess is now, as Derbyshire calls it, the "great white whale" of mathematical research.

The character of Bernhard Riemann really moved me. Terribly shy, always in poor health to primarily to poverty, philosophically- and religiously-minded (his father was a Lutheran minister and Bernhard came to college with the intent of studying theology). Yet undoubtedly brilliant and bold, and greatly admired by his friends and colleagues. Like too many geniuses, Bernhard was doomed to an early death (tuberculosis, at age 39). Also in the mix are the colorful personalities that are revealed when one studies any subject in depth: Euler, Gauss, Dirichlet, Dedekind, and a handful of others, Riemann’s predecessors and contemporaries, all leading up to the quest to solve the hypothesis.

The math is handled in a very easy and gradual way. It’s half-way through the book before we even get to the Hypothesis; the first half’s odd-numbered chapters laying down the necessary background. I’m no expert and can’t provide a satisfactory concise explanation of the Problem off the cuff here, but suffice it to say I understand where the Derb was leading me, and it fired my imagination. Plus, it made me want to explore what I’d learned, especially series, a topic I’ve never formally studied in school. That alone, for an author, is probably the best praise one can get.

Bottom line: Prime Obsession is a superb introduction to the greatest unsolved problem in mathematics today. Grade: A.