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Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.
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.
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.
Scientific data sets are becoming more dynamic, requiring new mathematical techniques on par with the invention of calculus.
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.