Algebraic number theory is a foundational branch of mathematics that investigates the properties of algebraic numbers and their relationships through the lens of field extensions and rings of integers ...

A vector $m = (m_1,\ldots, m_n) \in \mathbf{Z}^n\backslash\{0\}$ is called an integer relation for the real numbers $\alpha_1,\ldots, \alpha_n$, if $\sum \alpha_im_i ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, such ...

The vast majority of students won’t take algebra until middle or high school. But teachers can start laying the groundwork for this pivotal class a lot sooner, some researchers say—and instilling ...