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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.


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.

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.

Abstractions blog

How (Relatively) Simple Symmetries Underlie Our Expanding Universe

July 15, 2019

Although Einstein’s theory of space-time seems more complicated than Newtonian physics, it greatly simplified the mathematical description of the universe.


The Simple Idea Behind Einstein’s Greatest Discoveries

June 26, 2019

Lurking behind Einstein’s theory of gravity and our modern understanding of particle physics is the deceptively simple idea of symmetry. But physicists are beginning to question whether focusing on symmetry is still as productive as it once was.