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: ...

Most people rarely deal with irrational numbers—it would be, well, irrational, as they run on forever, and representing them accurately requires an infinite amount of space. But irrational constants ...

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 oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field.

“Do you see the pattern? Each number in the series after the first two numbers is the sum of the preceding two numbers.” That’s how I began my last column focusing on the Fibonacci sequence, which ...

Originally defined as the ratio between the circumference of a circle and its diameter, pi — written as the Greek letter π — appears throughout mathematics, including in areas that are completely ...

It's Pi Day! And in honor of this year's celebration I decided to do a bit of historical research. While π—the ratio between a circle's circumference and its diameter—has long been known and ...

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 ...

A new number theory paper comes from three academic researchers and, astonishingly, one prison inmate. Number theory is full of complex problems with applications in cryptography and more. The paper ...