Explainers

The math of data structures helps us understand how different storage systems come with different trade-offs between resources such as time and memory.

Try as they might, scientists can’t truly rid a space or an object of its energy. But what “zero-point energy” really means is up for interpretation.

By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools.

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.

Earth’s radiation can send some molecules spinning or vibrating, which is what makes them greenhouse gases. This infographic explains how relatively few heat-trapping molecules can have a planetary effect.

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, decomposes any function into its parts.

Fundamental technique lets researchers use a big, expensive “teacher” model to train a “student” model for less.

Every elementary particle falls into one of two categories. Collectivist bosons account for the forces that move us while individualist fermions keep our atoms from collapsing.

From living matter to molecules to elementary particles, the world is made of “chiral” objects that differ from their reflected forms.