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 ...

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 ...

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 ...

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, ...

We recently wrote about how infinitely large sets are not all the same size as each other, but we were a bit vague about what we meant by a set. The people who invented set theory also started out ...

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the ...

For a few months now, the mathematical world has been abuzz. Rumors abound of a new proof, monumental in length and virtually ...