The proof resolves a nearly 80-year-old problem known as the Duffin-Schaeffer conjecture. In doing so, it provides a final answer to a question that has preoccupied mathematicians since ancient times: ...

A smarter way to find π using fake circles. This short shows a clever geometric idea that estimates pi without perfect circles, revealing why the method works and how approximation can beat precision.

Later mathematicians discovered an even better and nearly as concise approximation for pi: 355/113. “It’s hard to write down what pi is,” said Ben Green of Oxford. “What people have tried to do is to ...