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: ...

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 ...

一、Approximate Number Sense托福听力原文： NARRATOR:Listen to part of a lecture in a psychology class. FEMALE PROFESSOR:For some time now,psychologists have been aware of an ability we all share.It's the ...

The deep recesses of the number line are not as forbidding as they might seem. That's one consequence of a major new proof about how complicated numbers yield to simple approximations. The proof ...