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 ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

At first glance, the problem seems ridiculously simple. And yet experts have been searching for a solution in vain for decades. According to mathematician Jeffrey Lagarias, number theorist Shizuo ...