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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.

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

By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations.

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?

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

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

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.

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