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symmetry

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.

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.

Diagram showing a colorful visualization of the simple Lie group
Abstractions blog

The ‘Useless’ Perspective That Transformed Mathematics

June 9, 2020

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

April 20, 2020

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.

Abstractions blog

Neutrino Asymmetry Passes Critical Threshold

April 15, 2020

The first official evidence of a key imbalance between neutrinos and antineutrinos provides one of the best clues for why the universe contains something rather than nothing.

Multimedia

The Map of Mathematics

February 13, 2020

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Illustration of a pair of lungs being scanned in three dimensions, with a status bar that reads “Scanning lung tissue: 60%.”
artificial intelligence

An Idea From Physics Helps AI See in Higher Dimensions

January 9, 2020

The laws of physics stay the same no matter one’s perspective. Now this idea is allowing computers to detect features in curved and higher-dimensional space.

A domino, a two of clubs, and a clock face.
Abstractions blog

Why the Laws of Physics Are Inevitable

December 9, 2019

By considering simple symmetries, physicists working on the “bootstrap” can rediscover the basic form of the known forces that shape the universe.

An interactive illustration of shapes hiding clocks.
cosmology

Cosmic Triangles Open a Window to the Origin of Time

October 29, 2019

A close look at fundamental symmetries has exposed hidden patterns in the universe. Physicists think that those same symmetries may also reveal time’s original secret.