When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.

# Articles tagged topology

### Nobel Prize Awarded for Quantum Topology

Three physicists have been awarded the Nobel Prize in Physics for rewriting our understanding of exotic quantum states on the surfaces of materials.

### 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?

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to 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 has become the first woman Fields medalist for drawing deep connections between topology, geometry and dynamical systems.