When I tell someone I am a mathematician, one of the most curious common reactions is: “I really liked math class because everything was either right or wrong. There is no ambiguity or doubt.” I ...

In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history. Mathematicians of the era sought a solid foundation for mathematics: a set ...

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 ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

The starting point for rigorous reasoning in mathematics is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. It is usually self-evident, for example, ...

Every day, dozens of like-minded mathematicians gather on an online forum called Zulip to build what they believe is the future of their field. They’re all devotees of a software program called Lean.

This photograph does a pretty good job of "describing" ripples. But a mathematician could do it with greater precision and predictive power. Image credit: andressolo, Flickr, CC BY 2.0 "How is it ...

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, ...

Veritasium A mathematical statement everyone believes but no one can prove Posted: January 7, 2026 | Last updated: January 7, 2026 Some mathematical statements feel undeniably true the moment you hear ...