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To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry.

The nervous systems of foraging and predatory animals may prompt them to move along a special kind of random path called a Lévy walk to find food efficiently when no clues are available.

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?

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