A problem at the interface of two mathematical areas, topology and algebraic geometry, that was formulated by Friedrich Hirzebruch, had resisted all attempts at a solution for more than 50 years. The ...

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 ...

Special number sequences—such as Fibonacci, Lucas, Horadam and Jacobsthal families—exhibit rich algebraic structures that underpin a broad spectrum of mathematical theory and application. At their ...

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, ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

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 ...

A mathematician has built an algebraic solution to an equation that was once believed impossible to solve. The equations are fundamental to maths as well as science, where they have broad applications ...

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 ...