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520px photo of Robert Langlands
Abstractions blog

Robert Langlands, Mathematical Visionary, Wins the Abel Prize

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

Portrait of Mathematician Prof. Günter M. Ziegler

In Search of God’s Perfect Proofs

The mathematicians Günter Ziegler and Martin Aigner have spent the past 20 years collecting some of the most beautiful proofs in mathematics.

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.

520px illustration for scale=free networks
network science

Scant Evidence of Power Laws Found in Real-World Networks

A new study challenges one of the most celebrated and controversial ideas in network science.

520px illustration for herd immunity
Quantized Academy

How Math (and Vaccines) Keep You Safe From the Flu

Simple math shows how widespread vaccination can disrupt the exponential spread of disease and prevent epidemics.

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.

520px photo of Richard Schwartz

In Praise of Simple Problems

The mathematician Richard Schwartz finds the hidden depth lurking in simple mathematical puzzles.

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.