When a gang of gambling cheats sussed out how to beat the house, they inadvertently highlighted a loophole from a shuffled deck. It took a magician-turned-mathematician to reveal how.

Chaos and the Feigenbaum constant

A retired German man has found the proof to a complex geometry and probability problem that experts have tried to solve for decades, only for his achievement to go largely unnoticed.  Thomas Royen found the solution to the conjecture, known as the Gaussian correlation inequality (GCI). 

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures. By Kevin Hartnett.

A Ukrainian mathematician has solved the centuries-old sphere-packing problem in dimensions eight and 24. By Erica Klarreich.

What happens when someone claims to have proved a famous conjecture? Well, it depends. When a paper is submitted, the journal editor will pass it off to a respected expert for examination. That referee will then scan the paper looking for a significant new idea. If there isn’t one, then the whole argument is unlikely to get much more scrutiny.

This is truly amazing. By Fiona MacDonald.

Really succinct explanation of my (and everyone else's) favorite identity. Very KhanAcademy-esque.

Introduction to divergence theorem (also called Gauss's theorem), based on the intuition of expanding gas.