Geometry

The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.

Can you turn a two-dimensional fractal into a 3-D object? Break out your scissors and tape for a chance to win a 3-D printed sculpture.

By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations.

Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

Peter Scholze is a favorite to win one of the highest honors in mathematics for his contributions in number theory and geometry.

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.