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geometry

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.
Quantized Columns

Quantum Questions Inspire New Math

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

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

A Long-Sought Proof, Found and Almost Lost

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.
Abstractions blog

The Hidden Twist to Making a Möbius Strip

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.
geometry

A Fight to Fix Geometry’s Foundations

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.
Abstractions blog

How Curvature Makes a Shape a Shape

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.
Abstractions blog

Test Your Mathematical Sculpting Skills

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.
geometry

3-D Fractals Offer Clues to Complex Systems

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.
Abstractions blog

Air Traffic Control for Random Surfaces

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.
geometry

A Unified Theory of Randomness

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