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 ...

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

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 ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...

Is there an infinity of infinities? The question sounds almost absurd, like a child’s riddle meant to twist your brain into knots. But for mathematicians, it’s a serious (and endlessly fascinating) ...