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New Strides Made on Deceptively Simple ‘Lonely Runner’ Problem
A straightforward conjecture about runners moving around a track turns out to be equivalent to many complex mathematical questions. Three new proofs mark the first significant progress on the problem in decades.
Can the Most Abstract Math Make the World a Better Place?
Columnist Natalie Wolchover explores whether applied category theory can be “green” math.
The Man Who Stole Infinity
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.
The Evolving Foundations of Math
An exploration of how mathematicians are still renovating and rebuilding the core pillars of their field today.
How Can Infinity Come in Many Sizes?
Intuition breaks down once we’re dealing with the endless. To begin with: Some infinities are bigger than others.
Long-Sought Proof Tames Some of Math’s Unruliest Equations
Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.
Networks Hold the Key to a Decades-Old Problem About Waves
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.
Two Twisty Shapes Resolve a Centuries-Old Topology Puzzle
The Bonnet problem asks when just a bit of information is enough to uniquely identify a whole surface.
Using AI, Mathematicians Find Hidden Glitches in Fluid Equations
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.