Originally defined as the ratio between the circumference of a circle and its diameter, pi — written as the Greek letter π — appears throughout mathematics, including in areas that are completely ...

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer. The ...

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: ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...