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topology

Heavenly billiards
geometry

New Shapes Solve Infinite Pool-Table Problem

August 8, 2017

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

Maryam Mirzakhani
Quantized Columns

The Beautiful Mathematical Explorations of Maryam Mirzakhani

July 24, 2017

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

geometry

A Fight to Fix Geometry’s Foundations

February 9, 2017

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.

Abstractions blog

Nobel Prize Awarded for Quantum Topology

October 4, 2016

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

Abstractions blog

Air Traffic Control for Random Surfaces

August 5, 2016

Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.

geometry

A Unified Theory of Randomness

August 2, 2016

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

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profile

The Oracle of Arithmetic

June 28, 2016

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

Biology

How Strange Twists in DNA Orchestrate Life

January 5, 2016

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?

May 19, 2015

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.