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: ...

When my students grow too dependent on their calculators, I ask them to find a number that, when multiplied by itself, gives them 2. Students quickly see that since 1² = 1 and 2² = 4, the answer has ...

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 ...

Happy Pi Day! We celebrate pi on March 14 because 3-14 gives the first three digits of this famous number. But what’s the big deal about pi anyway? Why does it get a day? Well, for starters, it ...

When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works.

This article is adapted from Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else by Jordan Ellenberg. © Penguin Press 2021 ...

For centuries, one of algebra’s oldest puzzles has remained unsolved—how to find exact answers for higher-degree polynomials, where the variable is raised to the fifth power or more. Mathematicians ...

This Pi Day, as you’re enjoying your slice of pie, explore a bigger slice of mathematics. Most March 14 celebrations are obsessed with the number pi. If you think “obsessed” is too strong, take a look ...

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 ...

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 ...

When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works. Breaking space news, the latest updates on rocket launches, skywatching events and more! You are ...