Algebra provides the formal framework to describe mathematical structures such as groups, rings and fields, while number theory investigates the properties of integers and their extensions. At their ...

Algebraic number theory explores the arithmetic of algebraic numbers, emphasising both theoretical structures and computational strategies that enable explicit determination of key invariants. At its ...

An AI model by OpenAI has solved the 80-year-old planar unit distance problem, showcasing its potential to revolutionize research across mathematics and other scientific fields.

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 ...

Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF. §14.2 Algebraic Topology. Topology is generally introduced as I described it in §AG.6, ...

After an AI from OpenAI found a trick to solve an 80-year-old conjecture from Paul Erdős, mathematicians have borrowed the same technique to solve another important problem ...

The University of Colorado Center for Number Theory has interests spanning number theory, from analytic to algebraic. There is a focus on arithmetic geometry, including arithmetic dynamics, elliptic ...