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When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

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.