Prime Obsession is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis and some of its applications. It is written for a popular audience, so even though it includes college-level mathematics, rigorous proofs are not provided, and much is taken on faith. Much historical background is provided, starting from Carl Friedrich Gauss and continuing well into the twentieth century.
The text of the book can be read online, free of charge.
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