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Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

Mathematicians have found that materials conduct electricity when electrons follow a universal mathematical pattern.

In a world seemingly filled with chaos, physicists have discovered new forms of synchronization and are learning how to predict and control them.

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

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?

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