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geometry

Thomas Royen at his home in Schwalbach am Taunus, Germany.
statistics

A Long-Sought Proof, Found and Almost Lost

March 28, 2017

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

Mobius strip illustration
Abstractions blog

The Hidden Twist to Making a Möbius Strip

February 9, 2017

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

geometry

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.

Hyperbolic Crochet
Abstractions blog

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.

Julia Set Contest
Abstractions blog

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.

3D "Basilica" Julia set
geometry

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.

Abstractions blog

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.

geometry

A Unified Theory of Randomness

August 2, 2016

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

Abstractions blog

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.