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From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.

Emperor penguins display rigorously geometric spacing and mathematical efficiency when they huddle together for warmth, which may reveal secrets to their overall health.

The “pinball” model of a slipping fault line borrows from the mathematics of avalanches.

Ronald Rivest helped come up with the RSA algorithm, which safeguards online commerce. Now he’s hoping to make democratic elections more trustworthy.

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

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.

Psychedelic drugs can trigger characteristic hallucinations, which have long been thought to hold clues about the brain’s circuitry. After nearly a century of study, a possible explanation is crystallizing.

A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars.

Simple math can help scheming politicians manipulate district maps and cruise to victory. But it can also help identify and fix the problem.

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