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The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics.

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now.

Jelani Nelson designs clever algorithms that only have to remember slivers of massive data sets. He also teaches kids in Ethiopia how to code.

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

A numerical puzzle, a geometric puzzle and a game of random patterns — all with connections to the legendary mathematician — elicited an enthusiastic response from readers.

An exercise in pure mathematics has led to a wide-ranging theory of how the world comes together.

Struggling with math problems that can’t be solved helps us better understand the ones we can.

Bryna Kra searches for the patterns in sequences of numbers that explain how complicated dynamical systems evolve over time.

A cryptographic master tool called indistinguishability obfuscation has for years seemed too good to be true. Three researchers have figured out that it can work.