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Air Traffic Control for Random Surfaces
Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.
A Unified Theory of Randomness
Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.
The Oracle of Arithmetic
At 28, Peter Scholze is uncovering deep connections between number theory and geometry.
How Strange Twists in DNA Orchestrate Life
Coils and twirls in DNA’s double-helix change how the molecule behaves, opening a new role for topology in the study of life.
Will Computers Redefine the Roots of Math?
The Fields medalist Vladimir Voevodsky has died at 51. This 2015 article describes his computer-aided quest to eliminate human error and rewrite the century-old rules underlying all of mathematics.
A Proof That Some Spaces Can’t Be Cut
Mathematicians have solved the century-old triangulation conjecture, a major problem in topology that asks whether all spaces can be subdivided into smaller units.
Scientists Conjure Curves From Flatness
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.
A Tenacious Explorer of Abstract Surfaces
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.
The Mathematical Shape of Things to Come
Scientific data sets are becoming more dynamic, requiring new mathematical techniques on par with the invention of calculus.