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 ...

Computers are working to solve an age-old geometry problem. Humans can’t “square the circle” by hand, which was proven in the 1800s. Computer solutions involve infinity, complexity, and some ...

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 ...