In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries. Sphere packing might seem ...

Neuroscientists are exploring whether shapes like squares and rectangles — and our ability to recognize them — are part of what makes our species special. Credit...Video by Yoshi Sodeoka Supported by ...

This originally appeared in the July/August issue of Discover magazine as "Your Hyperbolic Mind." Support our science journalism by becoming a subscriber. The human brain is both a marvel and a ...