Where does require look for modules?

Because macros can change semantics of the core language constructs, you have to explicitly opt-in into using them. This was a very early design decision.

The order of compilation doesn’t matter with import because it is resolved at runtime. But the order of compilation matters with macros specifically because they happen at compile time.

Calling function happens at runtime, where modules are already compiled. For macros modules are required to be compiled in a certain order, a.k.a. the module with the macros must be compiled before the module using those macros. This dependency in compilation order is set up by using require or import.

require does not look for files at all, the module has to be already loaded

Why does elixir make you require a module before you can call the macros defined in the module? I don’t have to import a module before I call the functions defined in the module.

All require does is enables macros from that module. It doesn’t do anything else.

See the documentation: Kernel.SpecialForms — Elixir v1.20.2

Without a doubt you are causing yourself more headache than its worth. Create a new mix project and put the files in lib and call it a day. Mix makes this easy for this very reason.

require in Elixir is not like require in your prior language. That quote you included from @mgwidmann explains it well. require is about macros, and you’re not using macros.

Edit to add:
The getting started guide is a good place to … well .. get started. It covers require in more depth here: https://elixir-lang.org/getting-started/alias-require-and-import.html#require

I’m not using a mix project.

If you’re not using mix, then you need to compile by hand.

$ elixirc my_math.ex

Okay, that worked…but it also worked without the require statement, so I guess I don’t understand what require does yet:

As for the code you’ve written, you don’t need a require statement at all. Requires are for loading macros before they’re used, which your function is not (its just a plain function). You can remove the require MyMath and everything will still work fine.

The problem is that the book I’m reading hasn’t covered macros yet, but in the code examples there are lines with require, use, and import statements.

It’s not clear from what you’ve shown whether you’re in a mix project and whether you’ve compiled my_math.ex to generate a beam file. If you’re not using mix, then you need to compile by hand.

$ elixirc my_math.ex

will generate a file in the current directory called Elixir.MyMath.beam. Now that you have a beam file, it can be called in your exs script.

Doesn’t work:

~/elixir_programs$ ls -al my_lib.exs my_math.ex 
-rw-r--r--  1 7stud  staff  77 Aug 15 21:48 my_lib.exs
-rw-r--r--  1 7stud  staff  50 Aug 15 21:48 my_math.ex

~/elixir_programs$ iex my_lib.exs 
Erlang/OTP 20 [erts-9.3] [source] [64-bit] [smp:4:4] [ds:4:4:10] [async-threads:10] [hipe] [kernel-poll:false]

** (CompileError) my_lib.exs:2: module MyMath is not loaded and could not be found


~/elixir_programs$ cat my_lib.exs 
defmodule MyLib do
  require MyMath
  
  def go(), do: MyMath.calc(1, 2)
end

~/elixir_programs$ cat my_math.ex
defmodule MyMath do
  def calc(x, y), do: x+y
end