Prime Numbers and the Riemann Hypothesis

Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann Hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann Hypothesis.

Barry Mazur is Gerhard Gade University Professor of Mathematics at Harvard University, Massachusetts. He is the author of Imagining Numbers: (Particularly the Square Root of Minus Fifteen) and co-editor, with Apostolos Doxiadis, of Circles Disturbed: The Interplay of Mathematics and Narrative.

William Stein is Professor of Mathematics at the University of Washington. Author of Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach, he is also the founder of the Sage mathematical software project.