# ‘Prime Obsession’ by John Derbyshire

I must admit up front that biographical books are probably my most favourite genre overall! And I obviously like math. And this book is about two things: the Riemann Hypothesis and the mathematicians who have worked on it and the theories that revolve around it. When I found this book, it sounded like a great match and did not hesitate long to buy it.

The book’s odd chapters guide the reader, step by step, chapter by chapter, towards an understanding and maybe even appreciation of the Riemann Hypothesis. The even chapters give biographical background information about the main actors in analytic number theory from its very beginning.

It starts out with a discussion of infinite series and their convergence using the example of the harmonic series and the Leaning Tower of Lire in the first chapter. The second chapter introduces the life and person of Bernhard Riemann, the namesake of the hypothesis.

Later biographical chapters cover Gauss, Euler (both chapter 4), Dirichlet (chapter 6), Dedekind, Chebyshev (chapter 8), Hadamard (chapter 10), Hilbert (chapter 12), Hardy, Littlewood and Landau (chapter 14) and many other great mathematicians working in analytic number theory in the nineteenth and twentieth century.

The mathematical chapters range from an introduction to logarithms, complex numbers to the prime number theorem. Chapter 15 introduces Big O notation and the Möbius $\mu$ function. I have mentioned this particular example to demonstrate that the author does not shy away from explaining advanced concepts.

I was particularly pleased by the visual presentation of the values of the zeta function. The author not only plots the values of the zeta function on a segment of the real line $\zeta(x), x \in \mathbb{R}$, but in chapter 13, the author also introduces the Argument Ant and the Value Ant, two imaginary ants that walk the complex plane (either the domain or the co-domain) and produce values of the zeta function (or in the case of the Value Ant primage values). Special pre-image values that map to purely real or purely imaginary values are then plotted to give an impression of the behavior of the zeta function. This latte technique was new to me and I found it quite insightful.