Review of Prime Obsession

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The book traces the history and logic of efforts to prove the Riemann hypothesis, which concerns the following mathematical problem:  Is there a general rule for answering the question of how many prime numbers there are less than any given number? Three things help to make this math book accessible.  The first is the breezy conversational style.  For example, in describing the exact value of the infinite series 1 + 1/2 ² + 1/3 ² + …, the author says that it is not enough for mathematicians to know the sum to, say, six decimal places; they want an exact answer because they are "weird obsessives" and because an exact answer may shed new light on the underlying math (p 64).  The second element that makes this book accessible is its alternating chapters on technical and historical matters.  For example, in Chapter 11, entitled "Nine Zulu Queens Ruled China" (there is a reason for this crazy title!), the author introduces complex numbers, while in Chapter 12, entitled "Hilbert's Eighth Problem," he describes Hilbert (who, in an address in Paris in 1900, described 23 major unresolved mathematical problems, of which the eighth was the problem of prime numbers) as a keen dancer and a popular lecturer who took pleasure in strolls in the countryside while talking mathematics.  Finally, the third factor that makes this book accessible is its numerical examples.  For instance, the author gives the sum of the first 10 terms of the foregoing infinite series as 1.5497677… and then goes on to state that the sum of the first 10,000 terms is 1.6448340… (p. 64).  However, it would have been interesting at some point to see an example of a computational shortcut for this calculation. Otherwise, one envisions a person sitting with his or her calculator for five years to come up with such a number.

A number of math terms are explained, such as "function," "domain," "argument," "harmonic series," "convergence," "limits," and "continuity," but the author does manage to avoid calculus, for the most part. Notation is limited to a few Greek letters such as pi, sigma, eta, and zeta.

A high school math club or advanced math class could have fun with this book.  A family that does math games at home could also use the book.  The author states that the book is pitched to beginning college math majors.  The book clarifies the different fields of mathematics (arithmetic, geometry, algebra, and analysis) and provides insights that could be helpful in career exploration.