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: ...

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 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 ...

Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational constants ...

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...

Irrational numbers are numbers that cannot be expressed as the ratio of two whole numbers. This is opposed to rational numbers, like 2, 7, one-fifth and -13/9, which can be, and are, expressed as the ...

Why do irrational numbers exist? originally appeared on Quora: the place to gain and share knowledge, empowering people to learn from others and better understand the world. Answer by Alon Amit, PhD ...