Number Theory is one of the oldest branches of modern mathematics. It is motivated by the study of properties of integers and solutions to equations in integers. Many of its problems can be stated ...

The following content is now available. Source code and images are explained in details in the PDF accompanying these articles: Detecting Subtle Departures from Randomness, available here. I discuss, ...

Their ambitions were always high. When Will Sawin and Melanie Matchett Wood first started working together in the summer of 2020, they set out to rethink the key components of some of the most ...

The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...

A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n, the partitions of 3 ...

Every so often, the Pentagon's blue sky research arm gets slammed, for funding investigations that are a little too down-to-Earth. Then Darpa turns around, and sponsors a new project to "develop a ...

Definition: Number theory is a branch of pure mathematics devoted to the study of the natural numbers and the integers. It is the study of the set of positive whole numbers which are usually called ...