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mathematical physics

Mathematician Lauren Williams standing in front of a whiteboard that has mathematics written on it.

A Mathematician’s Unanticipated Journey Through the Physical World

December 16, 2020

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

Graphical model of a cubic earth.

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.

Illustration of a particle
Hidden Structure

What Is a Particle?

November 12, 2020

It has been thought of as many things: a pointlike object, an excitation of a field, a speck of pure math that has cut into reality. But never has physicists’ conception of a particle changed more than it is changing now.

water molecules, droplets and a wave
Abstractions blog

How Mathematical ‘Hocus-Pocus’ Saved Particle Physics

September 17, 2020

Renormalization has become perhaps the single most important advance in theoretical physics in 50 years.

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.

Animation of black hole formation.
mathematical physics

New Math Proves That a Special Kind of Space-Time Is Unstable

May 11, 2020

Einstein’s equations describe three canonical configurations of space-time. Now one of these three — important in the study of quantum gravity — has been shown to be inherently unstable.

Photo of Freeman Dyson standing in a meadow in front of a forest
Quantized Columns

Remembering the Unstoppable Freeman Dyson

April 13, 2020

Freeman Dyson — physicist, mathematician, writer and idea factory — died on February 28, but his vitality lives on.


The Map of Mathematics

February 13, 2020

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

A rogue wave and a sailboat.
fluid dynamics

The Grand Unified Theory of Rogue Waves

February 5, 2020

Rogue waves — enigmatic giants of the sea — were thought to be caused by two different mechanisms. But a new idea that borrows from the hinterlands of probability theory has the potential to predict them all.