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 ...

Our research group is concerned with two lines of investigation: the construction and study of (new) cohomology theories for algebraic varieties and the study of various aspects of the Langlands ...

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 mathematician has built an algebraic solution to an equation that was once believed impossible to solve. The equations are fundamental to maths as well as science, where they have broad applications ...