It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question. In June 1978, the ...

Most people learn to count and do basic arithmetic at a young age and don’t give these skills a second thought. But numerosity or numeracy, the ability to think about and use numbers, is more than a ...

In the early 1970s mathematician Donald Knuth spent a sabbatical with his wife in Norway. The time was meant to be spent relaxing. Yet one night he woke up his partner in a state of agitation. He ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. In October 2018, David Asperó was on holiday in Italy, gazing out a car ...