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dynamical systems

Classes of geometric structures
Abstractions blog

Why Mathematicians Like to Classify Things

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Heavenly billiards

New Shapes Solve Infinite Pool-Table Problem

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

3D "Basilica" Julia set

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.

complex systems

Nature’s Critical Warning System

Scientists are homing in on a warning signal that arises in complex systems like ecological food webs, the brain and the Earth’s climate. Could it help prevent future catastrophes?


A Twisted Path to Equation-Free Prediction

Complex natural systems defy analysis using a standard mathematical toolkit, so one ecologist is throwing out the equations.


Strange Stars Pulse to the Golden Mean

Nature has revealed peculiar mathematical objects that connect order and chaos.

2014 Fields Medal and Nevanlinna Prize Winners

A Tenacious Explorer of Abstract Surfaces

Maryam Mirzakhani, who became the first woman Fields medalist for drawing deep connections between topology, geometry and dynamical systems, has died of cancer at the age of 40. This is our 2014 profile of her life and work.

2014 Fields Medal and Nevanlinna Prize Winners

A Brazilian Wunderkind Who Calms Chaos

Artur Avila’s solutions to ubiquitous problems in chaos theory have “changed the face of the field,” earning him Brazil’s first Fields Medal.