What is the most bizarre real number that you can imagine? Probably many people think of an irrational number such as pi (π) or Euler’s number. And indeed, such values can be considered “wild.” After ...

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: ...

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, ...

There are many different types of numbers, some of which you may remember from school: natural, rational, irrational, imaginary, calculable and incalculable numbers. Today, however, we are going to ...

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 ...

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 ...

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 ...