Geometry

Whether you’re passing secret notes in class or downloading images from a space probe, Reed-Solomon codes offer an ingenious way to embed information and correct for errors.

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.

Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves.

Proving that two polygons have the same area can be as easy as cutting them up and rearranging the pieces.

Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio.

The decades-old Sullivan’s conjecture, about the best way to minimize the surface area of a bubble cluster, was thought to be out of reach for three bubbles and up — until a new breakthrough result.

A comprehensive mathematical framework treats wrinkling patterns as elegant solutions to geometric problems.

Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.