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 ...

With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary. The boundary does not pass between ...

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 ...

Black holes exist in our universe. That’s widely accepted today. Physicists have detected the X-rays emitted when black holes feed, analyzed the gravitational waves from black hole collisions and even ...

At the beginning of the 20th century, the German mathematician David Hilbert (1862–1943) advocated an ambitious program to formulate a system of axioms and rules of inference that would encompass all ...

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 ...