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 ...

Graduate students in algebra, number theory and algebraic geometry courses build upon knowledge first learned in grade school. These are the best math schools for algebra / number theory / algebraic ...

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 ...