Archive

Of all the endless questions children and mathematicians have asked about infinity, one of the biggest has to do with its size.

The past and the future are tightly linked in conventional quantum mechanics. Perhaps too tightly. A tweak to the theory could let quantum possibilities increase as space expands.

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

A new atomic-scale experiment all but settles the origin of the strong form of superconductivity seen in cuprate crystals, confirming a 35-year-old theory.

Field research suggests a new explanation for the synchronized flashing in fireflies and confirms that a novel form of “chimeric” synchrony occurs naturally.

A simple geometric idea has been used to power advances in information theory, cryptography and even blockchain technology.

A custom-built machine learning algorithm can predict when a complex system is about to switch to a wildly different mode of behavior.

Robots can surpass the limitations on how high and far animals can jump, but their success only underscores nature’s ingenuity in making the most of what’s available.

Richard Rusczyk, founder of Art of Problem Solving, has a vision for bringing “joyous, beautiful math” — and problem-solving — to classrooms everywhere.