At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the ...

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 ...

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, ...

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 them. Yet ...