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Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.

The mechanism behind leopard spots and zebra stripes also appears to explain the patterned growth of a bismuth crystal, extending Alan Turing’s 1952 idea to the atomic scale.

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

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.

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