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: ...

When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. At least 3,700 years ago, Babylonian mathematicians approximated the ratio of a circle's ...

The decimal expansion of pi goes on forever. But an infinite number of fractions can approximate it to ever-increasing accuracy.KuoCheng Liao/Quanta Magazine The deep recesses of the number line are ...