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 ...

"All Cretans are liars", said Epimenides, a Cretan. But this means that his statement must be a lie too. But then it is false that Cretans are liars and the statement must be true. So what now?

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 ...

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 ...

In mathematics, some theorems seem self‑evident yet remain unproven. Explore the story of the “obviously true” statement that has baffled experts for decades. 'No idea what you have unleashed': ...