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mathematical physics

Illustration of a black hole with a Cauchy horizon
general relativity

Mathematicians Disprove Conjecture Made to Save Black Holes

Mathematicians have disproved the strong cosmic censorship conjecture. Their work answers one of the most important questions in the study of general relativity and changes the way we think about space-time.

Photograph of Albert Einstein in his office at the University of Berlin, published in the USA in 1920.
Abstractions blog

How Einstein Lost His Bearings, and With Them, General Relativity

By 1913, Albert Einstein had nearly completed general relativity. But a simple mistake set him on a tortured, two-year reconsideration of his theory. Today, mathematicians still grapple with the issues he confronted.

Animated illustration of a black hole in a cube of jelly
mathematical physics

To Test Einstein’s Equations, Poke a Black Hole

Two teams of researchers have made significant progress toward proving the black hole stability conjecture, a critical mathematical test of Einstein’s theory of general relativity.

Photo of smoke
Abstractions blog

What Makes the Hardest Equations in Physics So Difficult?

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

Simulation of Kelvin-Helmholz Instability
fluid dynamics

Mathematicians Find Wrinkle in Famed Fluid Equations

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense.

Lucy Reading-Ikkanda/Quanta Magazine
Abstractions blog

The Math That Promises to Make the World Brighter

The color of LED lights is controlled by a clumsy process. A new mathematical discovery may make it easier for us to get the hues we want.

Svitlana Mayboroda
mathematical physics

Mathematicians Tame Rogue Waves, Lighting Up Future of LEDs

The mathematician Svitlana Mayboroda and collaborators have figured out how to predict the behavior of electrons — a mathematical discovery that could have immediate practical effects.

mathematical physics

Strange Numbers Found in Particle Collisions

An unexpected connection has emerged between the results of physics experiments and an important, seemingly unrelated set of numbers in pure mathematics.

string theory

The Strange Second Life of String Theory

String theory has so far failed to live up to its promise as a way to unite gravity and quantum mechanics. At the same time, it has blossomed into one of the most useful sets of tools in science.