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topology

Mathematics

A Proof That Some Spaces Can’t Be Cut

January 13, 2015

Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.

geometry

Scientists Conjure Curves From Flatness

January 6, 2015

Researchers have found a set of rules for imbuing flat surfaces with curvature, enabling them to form a virtually unlimited range of three-dimensional structures.

2014 Fields Medal and Nevanlinna Prize

A Tenacious Explorer of Abstract Surfaces

August 12, 2014

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.

Data Driven: The New Big Science

The Mathematical Shape of Things to Come

October 4, 2013

Scientific data sets are becoming more dynamic, requiring new mathematical techniques on par with the invention of calculus.

Mathematics

Getting Into Shapes: From Hyperbolic Geometry to Cube Complexes and Back

October 2, 2012

Thirty years after William Thurston articulated a grand mathematical vision, a proof by Ian Agol marks the end of an era in the study of three-dimensional shapes.