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geometry

Graphical model of a cubic earth.
geophysics

Scientists Uncover the Universal Geometry of Geology

November 19, 2020

An exercise in pure mathematics has led to a wide-ranging theory of how the world comes together.

Quantized Academy

Some Math Problems Seem Impossible. That Can Be a Good Thing.

November 18, 2020

Struggling with math problems that can’t be solved helps us better understand the ones we can.

Harvard professor L. Mahadevan stands in a slightly cluttered office, holding an apple and a jar containing a miniature brain
Q&A

A Scientist Who Delights in the Mundane

October 26, 2020

From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.

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.

Q&A

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
geometry

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.