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 ...

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core ...

Brain-imaging techniques have made it possible to explore the neural foundations of logical and mathematical cognition. These techniques are revealing more than simply where these high-order processes ...

No less a mind than Bertrand Russell, of Principia Mathematica fame, was responsible for this paradox, which opened a hole in math. It’s those barbers. The Barber Paradox shows that barbers are not to ...

What is pure mathematics? What do pure mathematicians do? Why is pure mathematics important? These are questions I’m often confronted with when people discover I do pure mathematics. I always manage ...