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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.

Diagram showing show the hierarchy of different classes.
Abstractions blog

A Short Guide to Hard Problems

July 16, 2018

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.

Photo of the sun
Abstractions blog

What Is the Sun Made Of and When Will It Die?

July 5, 2018

If and when physicists are able to pin down the metal content of the sun, that number could upend much of what we thought we knew about the evolution and life span of stars.

Photo of Ziegler's chalkboard
Abstractions blog

The Infinite Primes and Museum Guard Proofs, Explained

March 26, 2018

A simple, step-by-step breakdown of two “perfect” math proofs.

Photo of smoke
Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

January 16, 2018

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

Classes of geometric structures
Abstractions blog

Why Mathematicians Like to Classify Things

August 15, 2017

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Abstractions blog

The Tricky Translation of Mathematical Ideas

June 28, 2017

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.