In *Prime Obsession* Derbyshire does his best to make the Hypothesis
accessible to anyone, however, starting off with almost no assumptions,
even explaining powers and logarithms. He builds steadily up from there,
however: explaining infinite sequences and series and functions and
complex numbers and big oh notation, while introducing the Euler product
formula, the Prime Number Theorem, the Zeta function, the Möbius mu
function, and "the error term". Along the way he also manages to touch
on field theory, algebraic number theory, and links to quantum mechanics
and chaotic dynamics.

This mathematics is coupled with an account of the history of the Hypothesis and of associated work in number theory and complex analysis, with mathematical chapters alternating with historical ones. This doesn't restrict itself to Riemann, despite the subtitle, but describes both those whose work led up to his and the most prominent of his successors: notably Euler, Gauss, Dedekind, Hilbert, Landau, Hardy, Littlewood, de la Vallée Poussin, and Hadamard.

Never having delved into analytic number theory, I found a fair bit that
was new to me in *Prime Obsession*. I think it unlikely that many people
who start off not knowing what a logarithm is will get to the end of it,
but the more accessible material does comes first and the historical
account can be followed independently. Anyone with an interest in
mathematics who has had some exposure to calculus and complex numbers
should enjoy Derbyshire's presentation.

November 2013

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