[stallmanifold]

I did one of my undergrads in mathematics. For me the primary benefit of studying pure mathematics was that it greatly improved my ability to think clearly. Mathematics more than almost any other discipline (physics and philosophy are on par with maths here) has the power to remove conceptual clutter, teach you to capture the essence of a problem, and be a more careful thinker. I've always been a first principles thinker, and maths made me a much better one. There is a night and day difference in how you think between the beginning and end of a good undergraduate Real Analysis course.

Applied to software engineering, it (indirectly) improved my abilty to understanding what a piece of software needs to do and why it's there. It also improved my ability to discern what level of abstraction is appropriate to the problem at hand, and figure out what questions to ask. In short, mathematics changes the way you think in a very powerful way. The precise contents of what you learn in the subject aren't necessarily applicable to everyday software engineering outside of a few areas, but the way of thinking is eminently so. For a personal example of where mathematics does come up in programming in a direct way, I do hobby graphics programming, which necessitates fluency in elementary linear algebra and benefits from grasping vector calculus (if you want to understand how light transport works and where physically-based rendering algorithms come from).