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algebra

Animation showing two sets of tangrams cycling between identical squares and different shapes.
geometry

Mathematicians Cut Apart Shapes to Find Pieces of Equations

October 31, 2019

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

Quantized Academy

The (Imaginary) Numbers at the Edge of Reality

October 25, 2018

Odd enough to potentially model the strangeness of the physical world, complex numbers with “imaginary” components are rooted in the familiar.

Art for "Why Mathematicians Can’t Find the Hay in a Haystack"
Abstractions blog

Why Mathematicians Can’t Find the Hay in a Haystack

September 17, 2018

In math, sometimes the most common things are the hardest to find.

Belt trick illustration
Abstractions blog

The Strange Numbers That Birthed Modern Algebra

September 6, 2018

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

Illustration of a complex shape casting a shadow
geometry

Tinkertoy Models Produce New Geometric Insights

September 5, 2018

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

fidget spinners
Quantized Academy

Symmetry, Algebra and the Monster

August 17, 2017

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.

Q&A

Moonshine Master Toys With String Theory

August 4, 2016

The physicist-mathematician Miranda Cheng is working to harness a mysterious connection between string theory, algebra and number theory.

The mathematician Ken Ono in his office at Emory University in Atlanta.
Q&A

A Life Inspired by an Unexpected Genius

May 19, 2016

Greatness was always expected of Ken Ono. But as he struggled with his parents’ expectations, he found solace and inspiration in the life of two-time college dropout — and mathematical genius — Srinivasa Ramanujan, the subject of the film The Man Who Knew Infinity.

number theory

Mathematicians Chase Moonshine’s Shadow

March 12, 2015

Researchers are on the trail of a mysterious connection between number theory, algebra and string theory.