Mathematical thinking can be extremely useful for programmers who never touch 3d games, or physics engines, or anything else requiring calculus or matrices. Fun

Mathematical thinking can be extremely useful for programmers who never touch 3d games, or physics engines, or anything else requiring calculus or matrices. Functions are mathematical objects, and can be combined using operators that obey mathematical laws into other functions - thinking of them in this way leads to the functional and concatenative programming paradigms. These combinations can also be rearranged in ways that also behave mathematically (i.e. according to simple rules that do not change, and have been explored for millenia), making it much easier to both refactor and optimize code. They can even be used as foundational abstractions for organizing your code, leading to horizontal rather than vertical abstraction - i.e., using the tower of abstract algebra or category theory types, we can organize our code in a way that anyone who understands that type will immediately grasp, whether or not they understand the internals. Math is everywhere, and you're using it, whether you know it or not. Might as well use it well.