The idea that a hidden fourth dimension could be woven into everyday reality is no longer just a science‑fiction trope. Leading theorists now argue that extra dimensions are not only compatible with ...

In 1611 German mathematician Johannes Kepler made a conjecture about the densest way to stack oranges or other spheres with a minimum of space between them. It seemed nothing could beat the standard ...

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible. If you’ve ever been stuck in traffic on a rainy afternoon, you’ve probably watched raindrops ...

This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American Earlier this year, Maryna Viazovska showed ...