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dynamical systems

Animated line drawing of Margaret Hamilton, Ellen Fetter, and a Lorenz attractor
chaos theory

The Hidden Heroines of Chaos

The story of the birth of chaos theory has left out two programming pioneers.

Art for "Brains Speed Up Perception by Guessing What’s Next"

Brains Speed Up Perception by Guessing What’s Next

Your expectations shape and quicken your perceptions. A new model that explains how that happens also suggests it’s time to update theories about sensory perception and decision making.

Art for "Proof Finds That All Change Is a Mix of Order and Randomness"
dynamical systems

Proof Finds That All Change Is a Mix of Order and Randomness

All descriptions of change are a unique blend of chance and determinism, according to the sweeping mathematical proof of the “weak Pinsker conjecture.”

Photo illustration of Akshay Venkatesh
2018 Fields Medal and Nevanlinna Prize Winners

A Number Theorist Who Bridges Math and Time

Akshay Venkatesh, a former prodigy who struggled with the genius stereotype, has won a Fields Medal for his “profound contributions to an exceptionally broad range of subjects in mathematics.”

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.