Properly-done OOP is all about abstraction and reasoning. You're taking a set of concepts (business concepts, technical concepts, etc) and building a (hopefully) consistent model of how those concepts relate to each other. Included in this model is a deep understanding of the operations that can be performed on the model you've come up with. If you've done a good job about specifying the abstraction, you end up with a system that is easy to reason about. "If I do this, this will happen."
This is, in essence, the same thing you're doing with abstract algebra; you're looking at common behaviours of different systems, and building up a consistent model that works for all of them, including the operations that you can do. The underlying details may be different for vector addition and matrix multiplication, but, using abstract algebra, you can reason about the behaviour in the same way.
Good OOP has the same effect.
Properly-done OOP is all about abstraction and reasoning. You're taking a set of concepts (business concepts, technical concepts, etc) and building a (hopefully) consistent model of how those concepts relate to each other. Included in this model is a deep understanding of the operations that can be performed on the model you've come up with. If you've done a good job about specifying the abstraction, you end up with a system that is easy to reason about. "If I do this, this will happen."
This is, in essence, the same thing you're doing with abstract algebra; you're looking at common behaviours of different systems, and building up a consistent model that works for all of them, including the operations that you can do. The underlying details may be different for vector addition and matrix multiplication, but, using abstract algebra, you can reason about the behaviour in the same way. Good OOP has the same effect.