Mathematics

In an 1874 paper, Georg Cantor proved that there are different sizes of infinity and changed math forever. A trove of newly unearthed letters shows that it was also an act of plagiarism.

Intuition breaks down once we’re dealing with the endless. To begin with: Some infinities are bigger than others.

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.

Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal.

The Bonnet problem asks when just a bit of information is enough to uniquely identify a whole surface.

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, researchers have found a slew of new candidates in simpler versions of the problem.

Explore a shape that can’t pass through itself, a teenage prodigy, and two new kinds of infinity.

Years ago, an audacious Fields medalist outlined a sweeping program that, he claimed, could be used to resolve a major problem in algebraic geometry. Other mathematicians had their doubts. Now he says he has a proof.

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