Comment by jillesvangurp

Certain fields need it more than others. Graphics and vide game development needs more math than web app development (well, usually. Sometimes you need to implement a formula), including trigonometry.

I used a bunch of trigonometry when I was making 2D action games, getting characters to move about the screen and move smoothly at all sorts of angles, for one example. I also used Sine functions a lot for UI animations, making things looks like they're hovering or oscillating up and down.

I think one of the benefits of these classes, though, and university classes in general, is that even if you don't use or really remember the specifics decades later, you're at least aware of how these problems can be solved, and can look up and verify potential solutions much quicker than if you hadn't ever been exposed to it at all.

There's value in "being able to master that stuff," and there's value in "having mastered that stuff." The latter lets you trim a lot of possible designs from your search space nearly instantly, letting you focus on routes which are actually viable. The former is only of similar power when you know the design in advance or there aren't many possible solutions.

For a simple example, suppose you need to operate on `n` permutations of an enormous collection of data (far more than fits in RAM or disk), and you need those permutations to be re-usable.

One simple solution is to shuffle the indices `n` times and store the results in your cluster, but even the shuffle process is slow with normal techniques because of inter-machine random-access bandwidth issues. When using those shuffled indices for anything, you're again bandwidth-limited if the task doesn't require access of every index.

With just a tiny bit of a math background, you'll recognize that an O(1)-state shuffle is possible, where you can create some `Permutation` object with a `permute()` method, taking in an index and outputting the corresponding index in your hypothetical shuffle. That permutation will be CPU-bound rather than bandwidth-bound.

The problem with "being able to master stuff" is that your search process in the design space is slow. If I went and told you that an O(1)-state shuffle existed and would be good for the problem, sure, you'd be able to go code that up without issues. What's the chance that you'd even know to try though?

> wide range of esoteric topics ... prepares you for a lifetime of learning

That's part of it, but each of those esoteric topics also give new ideas something to latch onto. Our brains are associative, and being able to look at a new thing and tie it to a few esoteric concepts is a bit of a superpower, even if the association is weak. The difference between knowing nothing other than how to learn and knowing what's vaguely potentially possible or not is weeks or months of research. It's the difference between having to do the dumb, slow thing and being the person promoted for saving $1m/yr fixing whatever you wrote. You can get by for a long time, maybe your entire career, just making shit work, but if you're looking for more money or prestige then there are better routes.

> IMHO math in general is overrated for general purpose programming. I had plenty of math in college in the early nineties. I rarely need or use any of it. And when I do, I need to look up a lot of stuff

The value isn't in knowing how to do math, it's in knowing when.

The value of a math class is far less in learning and remembering exactly how and, far more in learning what you can do with it so you can spot possible solutions when they arise. Expanding your mental toolkit.

There are lots of things that we should collectively be doing as an industry but, largely, aren't.