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 ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...

Catalan numbers, a distinguished sequence in combinatorial mathematics, consistently emerge in a wide range of counting problems—from enumerating binary trees and Dyck paths to counting possible ...

One of the titans of Number Theory—the study of natural numbers and their properties—is Diophantus of Alexandria, an ancient Greek mathematician who still pops up in algebra textbooks today. You might ...

What is your favorite number? For many people, it may be an irrational number such as pi (π), Euler’s number (e) or the square root of 2. Even among the natural numbers (positive integers), there are ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

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) ...