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geometry

Photo of two mathematicians drawing on a chalkboard
topology

Mathematics as a Team Sport

March 31, 2020

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

Multimedia

What Is the Geometry of the Universe?

March 16, 2020

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.

Photo of a complicated knot.
Abstractions blog

Color-Changing Material Unites the Math and Physics of Knots

February 10, 2020

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

Quantized Academy

How Simple Math Can Cover Even the Most Complex Holes

January 8, 2020

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.

Animation showing two sets of tangrams cycling between identical squares and different shapes.
geometry

Mathematicians Cut Apart Shapes to Find Pieces of Equations

October 31, 2019

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

foundations of mathematics

With Category Theory, Mathematics Escapes From Equality

October 10, 2019

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

Abstractions blog

How Randomness Can Make Math Easier

July 9, 2019

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

geometry

Random Surfaces Hide an Intricate Order

July 2, 2019

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

Q&A

A Mathematician Whose Only Constant Is Change

June 13, 2019

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