Ask HN: Did studying proof based math topics make you a better programmer?

For the things I've programmed, I barely needed any math. I found it more beneficial to study things like systems architecture and computer science. Knowing theories behind data structures, functional/imperative programming, algorithms, networking, file manipulation and more, that was the sort of thing I studied and exercised in my programming days.

For the record, I programmed Unix systems and services in C, Bourne shell, Perl, and similar languages. That was my professional career. Of course I got a real early start with BASIC, LOGO, and a little bit of assembly.

I was long considered "bad at math," a thing my dad said about himself* and an excuse that I readily took on when I got bad grades. I got a career in web development straight out of high school, and that carried me for several years until I got bored and resumed community college classes for enrichment. I took calculus and a beginning algorithms/data structures class my first semester. At the time, I still wasn't ready to jump back into calculus, and only showed up to the algorithms class. I was intrigued -- proofs had a direct application to my life! Later I would realize that programming taught me the basics of rigor and abstraction in a language I was willing to hear.

Thus began my mathematics career. I always had one foot in the computer science, and one foot in the mathematics. The proofs I saw in analysis were... fine, I guess, I got good grades because I did my homework with enough time to focus on it. But William exposed me to a world of computational mathematics that really carried my interest. From there, I learned new classes of algorithms, hairy implementation details, and more. My experience there was incredibly beneficial to my programming experience.

So my path was crooked: programming, then math, then back to programming. It is undeniable that these skills are heavily intertwined. Even if that undergrad analysis course feels like an inapplicable stumbling block along the way. Most mathematicians I know only used calculus to hone their symbolic manipulation skills.

* parents: watch your &$%&@@&$ mouth

I understand that countless engineers have this opinion, but really (and bluntly) all it means is that you’re unaware or ignorant of how maths applies to what you’re doing.

Abstract algebra has little prerequisites, so you can definitely do that. However, if calculus clicked with you, then you may find real analysis more to your liking. If you've done enough physics/engineering that requires calculus, you probably won't have trouble connecting the analysis material to your experience.

For me (engineering/physics), abstract algebra was ... abstract. It felt like a bunch of abstract ideas and structures that mathematicians invented to occupy themselves. Of course, that's not at all true in reality, but it was mostly irrelevant to my real world problems.

PS: If you've forgotten your calculus, don't worry - most real analysis courses/books start from scratch and don't assume prior knowledge.

I mean, sure, algorithms involve math. If you're dealing with trees/graphs, that's math. If you're compiling a program there is math behind the scenes. But for the majority of SW engineers, actually knowing the math is of little benefit to most problems that SW engineers need to solve. As long as you know the rudiments of algorithmic complexity (big Oh notation, etc), you're good.

(I am excluding trivial things like arithmetic and very basic algebra, as clearly this submission is speaking of more advanced math).