In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics.

"The appearance of such structures sheds new light on the sorts of mathematical objects that nature is built from." When you purchase through links on our site, we may earn an affiliate commission.

Oftentimes, we think of space as an endless, mostly empty vacuum, a silent backdrop where planets, stars, and galaxies play out their dance. We also think of time as something separate, a steady ...