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topology

geometry

A Fight to Fix Geometry’s Foundations

By Kevin Hartnett
February 9, 2017
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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

By Michael Moyer
October 4, 2016
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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

By Jeanette Kazmierczak
August 5, 2016
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Mathematicians have had a hard time finding commonalities in large groups of random shapes — until recently.

geometry

A Unified Theory of Randomness

By Kevin Hartnett
August 2, 2016
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Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures.

profiles

The Oracle of Arithmetic

By Erica Klarreich
June 28, 2016
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At 28, Peter Scholze is uncovering deep connections between number theory and geometry.

Biology

How Strange Twists in DNA Orchestrate Life

By Emily Singer
January 5, 2016
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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?

By Kevin Hartnett
May 19, 2015
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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

By Kevin Hartnett
January 13, 2015
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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.

geometry

Scientists Conjure Curves From Flatness

By Natalie Wolchover
January 6, 2015
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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.


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