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 ...

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 ...

Some mathematical statements feel undeniably true the moment you hear them. Yet proving them can be impossible. This theorem has convinced generations of mathematicians without ever yielding a formal ...

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite. Of all the tools available to the mathematician, randomness would seem to offer little ...

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.