Prime Numbers and the Riemann Hypothesis

March 2015 Version

(currently in production for publication by Cambridge University Press)

Barry Mazur and William Stein

  PDF of the Book

  Slides from a talk

The Riemann Hypothesis is one of the great unsolved problems of mathematics and the reward of $1,000,000 of Clay Mathematics Institute prize money awaits the person who solves it. But-with or without money-its resolution is crucial for our understanding of the nature of numbers.

There are several full-length books recently published, written for a general audience, that have the Riemann Hypothesis as their main topic. A reader of these books will get a fairly rich picture of the personalities engaged in the pursuit, and of related mathematical and historical issues.

This is not the mission of the book that you now have before you. We aim-instead-to explain, in as direct a manner as possible and with the least mathematical background required, what this problem is all about and why it is so important.

See also the Github repository (with LaTeX source and Sage code).

This book is based upon work supported by the National Science Foundation under Grant No. 0653968. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This book will be published by Cambridge University Press.