On a recent train trip from Lyon to Paris, Vladimir Voevodsky sat next to Steve Awodey and tried to convince him to change the way he does mathematics. Voevodsky, 48, is a permanent faculty member at ...

The equal sign is the bedrock of mathematics. It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is ...

Let the physical basis of a social economy be given— or, to take a broader view of the matter, of a society. According to all tradition and experience human beings have a characteristic way of ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

By replacing the most fundamental concept in topology, Peter Scholze and Dustin Clausen are taking the first step in a far ...