By encoding mathematical statements into numbers, mathematician Kurt Gödel used ordinary arithmetic to check whether a ...

A statement can be true or false. But as Kurt Gödel demonstrated, there will always be mathematical assumptions that can ...

A mathematical statement everyone believes but no one can prove Some mathematical statements feel undeniably true the moment you hear them. Yet proving them can be impossible. This theorem has ...

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 ...