Algebraic structures and linear maps form a cornerstone in modern mathematics, underpinning areas as diverse as abstract algebra and functional analysis. Algebraic structures such as groups, rings ...

Algebraic topology: The study of topological spaces with methods from abstract algebra, emphasising the transformation of geometric problems into algebraic ones. Homotopy theory: ...

There’s no Nobel Prize in mathematics, but math undergirds much high-level science. The 2016 Nobel in Physics rewards work in topology, a branch of math with multiple real world applications.