Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. (See the list of number theory topics.)
The Riemann hypothesis, first formulated by Bernhard Riemann in 1859, is one of the most famous and important unsolved problems in mathematics. It has been an open question for almost 150 years, despite attracting concentrated efforts from many outstanding mathematicians. Unlike some other celebrated problems, it is more attractive to professionals in the field than to amateurs.
The Riemann hypothesis (RH) is a conjecture about the distribution of the zeros of the Riemann zeta-function ζ(s). The Riemann zeta-function is defined for all complex numberss ≠ 1. It has zeros at the negative even integers. These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that the real part of any non-trivial zero of the Riemann zeta function is ½.