# Algebra * Algebra is concerned with numbers and equations * When we start assigning numbers to things (for example, to topological spaces) we are assigning *algebraic structure*. If you can then *combine* these structures (e.g. via addition or subtraction), that is the beginning of algebra. > Algebra is a very flexible subject, and to define what an algebra is in full generality you need the collection of elements that you’re considering, and then you can specify arbitrarily many operations, with arbitrary errorities and you can specify arbitrarily many rules between them. And the subject of universal algebra invites you to consider examples like that. (mindscape podcast, emily riehl) > So what is it? So it’s some algebraic structure where I’m gonna start with the set of all points in the space. So I’ve forgotten the topology, I’ve forgotten about distances and stuff, I’m just remembering the set of points, ’cause in algebra, I have sort of sets and stuff, I don’t have geometry. So I’ve just remembered the set of the points in the space, then what I’m gonna throw in is the data of every possible path between any points in this space. This is gonna be a very big thing, by the way, so we’re covering out every possible path that an ant could take between points in the space, plus the composition. (mindscape podcast, emily riehl) --- Date: 20211012 Links to: [Mathematics MOC](Mathematics%20MOC.md) Tags: References: * [Mindscape podcast, Emily Riehl on topology (she touches on algebra)](https://www.preposterousuniverse.com/podcast/2021/05/10/146-emily-riehl-on-topology-categories-and-the-future-of-mathematics/)