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Aerial image of a complicated road network.
Abstractions blog

A New Algorithm for Graph Crossings, Hiding in Plain Sight

September 15, 2020

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

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.

A comically long “missing persons” poster for an odd perfect number that shows all the restrictions it has to satisfy.
number theory

Mathematicians Open a New Front on an Ancient Number Problem

September 10, 2020

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.


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

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

Illustration of a robot and a human furiously doing math next to each other
artificial intelligence

How Close Are Computers to Automating Mathematical Reasoning?

August 27, 2020

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

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.

An animation of a particle collision
Abstractions blog

The Mathematical Structure of Particle Collisions Comes Into View

August 20, 2020

Physicists have identified an algebraic structure underlying the messy mathematics of particle collisions. Some hope it will lead to a more elegant theory of the natural world.

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.