At the frontiers of theoretical physics, many of the most popular ideas have one thing in common: they begin from a mathematical framework that seeks to explain more things than our currently ...

Mathematics is one of the oldest disciplines of study. For all its antiquity, however, it is a modern, rapidly growing field. Only 70 years ago, mathematics might have been said to consist of algebra, ...

The field of Reverse Mathematics explores the minimal axiomatic frameworks necessary to prove classical theorems, seeking to elucidate the logical foundations of mathematics. In parallel, ...

Emily Riehl thinks hard about objects that don't exist in the material world yet mysteriously seem to underlie many things that do. These objects have no concrete existence of their own, but they do ...

Most economists subscribe to a belief in “positive economics,” which means that economic theory flows from economic data. Thus, all theory can be tested for ...

A mathematical proof has finally debunked the idea that we live in a simulation, according to a group of international researchers. The theory that the universe could be a computer programme has been ...