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 ...

OpenAI has revealed a breakthrough proof that overturns a nearly 80-year-old geometry conjecture posed by Paul Erdős.

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 ...

An OpenAI AI has brought mathematics one step closer to solving a famous Erdős problem. Researchers have been stuck on this ...

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, ...

The Canadian mathematician Robert Langlands has won the 2018 Abel Prize—one of mathematics’ most-prestigious awards—for discovering surprising and far-ranging connections between algebra, number ...

Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what ...

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 ...