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Geometry

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A Fight to Fix Geometry’s Foundations

February 9, 2017

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.

How Curvature Makes a Shape a Shape

January 9, 2017

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

Test Your Mathematical Sculpting Skills

January 5, 2017

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.

3-D Fractals Offer Clues to Complex Systems

January 3, 2017

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

Air Traffic Control for Random Surfaces

August 5, 2016

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

A Unified Theory of Randomness

August 2, 2016

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

Handicapping the 2018 Fields Medal

June 28, 2016

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

The Oracle of Arithmetic

June 28, 2016

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

Sphere Packing Solved in Higher Dimensions

March 30, 2016

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

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