Where does require look for modules?

require does not look for files at all, the module has to be already loaded in order for it to work in the way you are trying. If you add to the top of your file Code.require_file("my_math.exs"), you should see it start working. If you do $ mix new my_project and put these files in lib (as .ex files not .exs) you won’t need to do anything and the compiler will find the right file automatically; this is the typical way to do things. After that, run $ iex -S mix and your code will be available for execution (type into the prompt MyLib.go()).

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.
You can read more about alias, require, import and use here: https://elixir-lang.org/getting-started/alias-require-and-import.html

Related to this: A file containing a module with a name like Foo.Bar.Baz is placed in foo/bar/ and named baz.ex by convention, but there is nothing stopping you from doing it differently (except the very strong argument of confused coworkers).

Sometimes there are reasons for not following this convention though, for instance when having (for programmatic reasons) to define multiple modules in the same file.

You should be using *.ex files not *.exs files. The latter are only compiled in memory and beam files are not written to disk, which is why MyMath cannot be found. For a minimal fix, just rename my_math.exs to my_math.ex

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

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.

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.

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

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.

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

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

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.