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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.

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.

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

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

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

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

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

Corina Tarnita deciphers bizarre patterns in the soil created by competing life-forms.

Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?