This 180-sided object cannot fit through another like it, no matter where you bore the hole or how you tilt it.

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

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 ...

One hundred twenty years after it was first discovered, mathematicians have successfully mapped out a 248-dimensional object called E8. The complete description of E8—one of the most complicated ...