I have degrees in Math (PhD), CS(MS), and Engineering(BS). I find wonderful interactions between all three.

My career is a bit mixed up: Taught Math at a college (part time on and off for 10 years), Meteorologist (only 2 years), Nuclear Engineer (only 2 years), Systems Engineering (7 years), Hedge Funds (15 years). I did a lot of ML/AI (20 years) mostly for Trading Stocks, Poker, Torpedos, and Satellites. I wrote about 100,000 lines of C++ and about 10,000 lines for each of the following: BASIC, Mathematica, Matlab, and Haskell.

Math is an integral a part of my life and my thinking. :)

If I get some time later, maybe I will try to write up a few stories.

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).

I'm a maths graduate who became a programmer too. In my experience there's very little direct application of the knowledge acquired during the degree, but the thinking process gained is totally relevant. Doing a maths degree is one of the best things that happened in my life, and it altered the way I think forever. Having said that, now that I do a little bit of AI (as everyone should), I start to see more and more math in the code I write.

Little slow replying to this one, but that's fortunately given 3 other people in a similar position to reply and I can't agree more with the sentiment. Have I used my knowledge of approximating PDEs using multi-variate finite element methods? No, not really - though it makes for some interesting conversations with meteorologists occasionally. Whether it's the deep understanding of logical constructs (everyone should know what the contrapositive is) or the ability to model a problem and remove cruft, the way of thinking a maths degree instills will be invaluable forever.