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 ...

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 ...

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 were his actual mathematical contributions?

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 general outlines and the methods employed by the author will be familiar to readers who have seen the first volume. He has made a study of standard works and papers by Bachmann, Hensel, Hubert, ...

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.

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 ...

Hirzebruch's problem at the interface of topology and algebraic geometry has occupied mathematicians for more than 50 years. A professor of mathematics at the Ludwig-Maximilians-Universitaet in Munich ...