Abstract:Number theory is one of the oldest branches of mathematics. The field is characterized by the precision and elegance of its statements. In this talk we shall explain how the hunt for order in the subject extends to understanding even seemingly chaotic phenomena such as error terms.

We will focus on one particular set of errors that arise in the theory of elliptic curves and modular forms. That these errors display remarkable order was first conjectured by Sato and Tate about 40 years ago. In a breakthrough last year, Richard Taylor (and his coauthors) showed that the Sato-Tate probability distribution holds in many cases.

In this talk we will describe this result, and along the way introduce the audience to some of the basic objects of study in number theory.