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Quanta’s In Theory video series returns with an exploration of a mysterious mathematical pattern found throughout nature.

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.

When a crystallographer treated prime numbers as a system of particles, the resulting diffraction pattern created a new view of existing conjectures in number theory.

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

A California housewife who in the 1970s discovered four new types of tessellating pentagons is dead at 94.

A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.

Like scientific puzzles, Bongard problems can lead you through a frustrating blind search until you find that simple, elegant rule that fits a seemingly random pattern.

For your frustration, joy and entertainment, our puzzle challenges you to find general patterns or rules based on seemingly random, specific examples.

New research has prompted a resurgence of interest in the patterning mechanisms Alan Turing proposed 60 years ago.

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