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When 50 mathematicians spend a week in the woods, there’s no telling what will happen. And that’s the point.

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

Mathematicians have studied knots for centuries, but a new material is showing why some knots are better than others.

No one knows how to find the smallest shape that can cover all other shapes of a certain width. But high school geometry is getting us closer to an answer.

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

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.

Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.