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 geometry and number theory intersect in the study of solutions to polynomial equations and their symmetries. Algebraic geometry provides a language of schemes and varieties to capture ...

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 ...

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, ...

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 ...

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 ...

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, ...

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.