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 ...

Imagine being asked to pick a number from 1 to 10. You are quite likely to pick a whole number; I have never seen someone do otherwise. But you could also pick the number pi, whose decimal expansion ...

The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is far from ...

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 ...

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, ...

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 Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century. Most people are ...

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 ...