I would tend to say: It's the basis of everything. Here are some examples that were not given in other comments: - Graph theory is pretty algebra-heavy, and gr

I would tend to say: It's the basis of everything. Here are some examples that were not given in other comments: - Graph theory is pretty algebra-heavy, and graphs are everywhere. - Static analysis, in particular abstract interpretation, relies heavily on vector spaces and various algebraic structures. - All the "highly functional" structures (you know, monads and the like) are an off-shot branch of algebra. - Patch theory (git, darcs and other versioning systems that rely on patches). You get nice stuff if you use algebraic properties (such as having your patch commutes and things like that).