What's up in

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

Equations, like numbers, cannot always be split into simpler elements.

A new idea is helping to explain the puzzling success of today’s artificial-intelligence algorithms — and might also explain how human brains learn.

City blocks help illustrate why walking randomly tends to take you away from your starting point.

Why is it that when you walk randomly, the more you walk, the farther you get from your starting point?

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

A potent theory has emerged explaining a mysterious statistical law that arises throughout physics and mathematics.