What's up in

topology

geometry

A Unified Theory of Randomness

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

profile

The Oracle of Arithmetic

At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

Biology

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.

foundations of mathematics

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.

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.

geometry

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.

2014 Fields Medal and Nevanlinna Prize Winners

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.

Data Driven: The New Big Science

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.

Mathematics

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

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.