What's up in


An abstract illustration showing broken tools, cubes, numbers and other abstract representations of impossible math
Quantized Columns

When Math Gets Impossibly Hard

September 14, 2020

Mathematicians have long grappled with the reality that some problems just don’t have solutions.


Conducting the Mathematical Orchestra From the Middle

September 2, 2020

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

An illustration of an ant walking in a straight line around a dodecahedron.
Abstractions blog

Mathematicians Report New Discovery About the Dodecahedron

August 31, 2020

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

Photo of Marijn Heule walking among computer processors
Abstractions blog

Computer Scientists Attempt to Corner the Collatz Conjecture

August 26, 2020

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

Illustration of floating metal cubes joining together, some of their faces yellow

Computer Search Settles 90-Year-Old Math Problem

August 19, 2020

By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.

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.

Quantized Academy

The Math of Social Distancing Is a Lesson in Geometry

July 13, 2020

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries.

Animation of different rectangles made by connecting four points on a colorful loop.

New Geometric Perspective Cracks Old Problem About Rectangles

June 25, 2020

While locked down due to COVID-19, Joshua Greene and Andrew Lobb figured out how to prove a version of the “rectangular peg problem.”

Illustration showing an austere number line on one side and various interesting objects on the the other, including a dodecahedron, an armillary sphere, flowers and plants.
Quantized Columns

The Two Forms of Mathematical Beauty

June 16, 2020

Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe.