Complex systems

Simple rules in simple settings continue to puzzle mathematicians, even as they devise intricate tools to analyze them.

For decades, a small group of mathematicians has patiently unraveled the mystery of what was once math’s most popular picture. Their story shows how technology transforms even the most abstract mathematical landscapes.

For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

If we want to understand complex constructions, such as ourselves, assembly theory says we must account for the entire history of how such entities came to be.

By replacing thousands of equations with just one, ecology modelers can more accurately assess how close fragile environments are to a disastrous “tipping point.”

Nikta Fakhri is adapting and extending concepts from physics to describe how tiny biological components give rise to living organisms.

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

A custom-built machine learning algorithm can predict when a complex system is about to switch to a wildly different mode of behavior.

Physicists have solved a key problem of robotic locomotion by revising the usual rules of interaction between simple component parts.