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 ...

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 ...

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 ...

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

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, ...

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 ...

You scrambled up a Rubik’s cube, and now you want to put it back in order. What sequence of moves should you make? Surprise: You can answer this question with modern algebra. You might remember ...

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 ...