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Online comment platforms can bring out the best — and the worst — in people. At the end of a tumultuous year, *Quanta*’s editors highlight some of our favorite things you had to say.

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

Today’s information age is only possible thanks to the groundbreaking work of a lone genius.

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

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.