Mathematics often helps us to think about issues that don’t seem mathematical. One area that has surprisingly far-reaching applications is the theory of sets. Sets are one of the most basic objects in ...

Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

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 ...