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

I received a Ph.D. in pure math (number theory) from Berkeley, and then worked as an academic mathematician for 20 years, so wrote a few dozen research papers and some books. My ability to write software for doing mathematics was obviously better as a result of studying mathematics, e.g., I started SageMath (https://sagemath.org) and wrote a big chunk of it.

Now I mostly do full stack web development (I have goals that require doing it), and I do often think about my programming informed by intuitions from topology and algebraic geometry (e.g., scopes in programming are like neighborhoods in topology). Having experience with formal logic and proofs also helps in reasoning about what code I'm looking at will do. Experience with rigorous mathematics also makes me more humble about just how difficult it is for anybody to ever reason correctly about anything.

I taught mathematics to many undergrads over the years, and I would recommend anybody interesting in a career in programming also learn at least the basics of group theory and abstract algebra. It's extremely beautiful, and probably different than the other mathematics you encountered, e.g., in high school or engineering courses. There's just so many beautiful and deep ideas in an intro abstract algebra course that aren't very difficult to learn. I initially got into mathematics when I was an undergrad browsing the programming section of a used bookstore, and found an abstract algebra book that was misfiled in the programming section.

The problem is the premise of the question.

Is “better programmer” a useful metric to problem solving? For a class of problems, probably.

Math and other hard sciences will probably give you a different perspective than a traditional CS education which may help with solving certain types of problems. Those may be programming related, or may be something else. Of course it may depend on the kind of person you are too.

In my opinion it’s worth pursuing whatever feels hard in terms of education, even if there’s not a rigorous CS education. You can always go into CS later.

Learning math helps develop your ability to hold large, complicated logical edifices in your head and to analyze them. There are different ways to develop this skill, doing math is one way to go about it. Programming is fundamentally about reasoning about large logical structures, so the skills carry over. The specific topics may not help, but then again, they might. Learning multivariable calculus and linear algebra will help you if you work in graphics, machine learning, etc. Note that these are huge subjects, and there’s always more to learn—much more than you can pick up in a semester or two at college.

How crucial it is for you to be able to accurately analyze large logical systems depends on the kind of programming you do. In many cases, it isn’t that important. I think I being comfortable with ambiguity, understanding how to satisfy multiple conflicting constraints, how to be political, etc. are probably much more valuable skills. Many programming jobs simply do not require you to be that technical to get your tasks done.

If you want to get good at something, you will get far more return on your time and effort investment if you just practice that thing rather than something tangentially related to it. If you want to get good at programming, practice programming not math. Math may help you but it won't help as much as practicing programming.

I think "learn B because it will help you do A better" type of advice often doesn't work. But "learn adjacent fields if they are interesting to you, time and energy permitting" may work, as they sometimes do yield unexpected benefits.

I am doing the opposite of what you are asking, as my day job is a mathematician, and I found my hobby of programming sometimes helpful.