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symplectic geometry

Abstractions blog

How Physics Found a Geometric Structure for Math to Play With

July 29, 2020

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

Multimedia

The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Art for "Three Decades Later, Mystery Numbers Explained"
Abstractions blog

Three Decades Later, Mystery Numbers Explained

May 3, 2018

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Illustration for "Mathematicians Explore Mirror Link Between Two Geometric Worlds"
geometry

Mathematicians Explore Mirror Link Between Two Geometric Worlds

April 9, 2018

Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.

Mobius strip illustration
Abstractions blog

The Hidden Twist to Making a Möbius Strip

February 9, 2017

The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.

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.