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

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 ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

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 ...

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, ...

Alan Turing, Albert Einstein, Stephen Hawking, John Nash—these “beautiful” minds never fail to enchant the public, but they also remain somewhat elusive. How do some people progress from being able to ...