Mathematics

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.

After more than three centuries, a geometry problem that originated with a royal bet has been solved.

The math of even the simplest ocean waves is notoriously uncooperative. A team of Italian mathematicians has made major advances toward understanding it.

The amplituhedron, a shape at the heart of particle physics, appears to be deeply connected to the mathematics of paper folding.

Using a relatively young theory, a team of mathematicians has started to answer questions whose roots lie at the very beginning of mathematics.

Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.

Climate science is the most significant scientific collaboration in history. This series from Quanta Magazine guides you through basic climate science — from quantum effects to ancient hothouses, from the math of tipping points to the audacity of climate models.

Building an accurate model of Earth’s climate requires a lot of data. Photography reveals the extreme efforts scientists have undertaken to measure gases, glaciers, clouds and more.

Tipping points in our climate predictions are both wildly dramatic and wildly uncertain. Can mathematicians make them useful?