Mathematica: HOWTO Autoload the simplest possible .m or .wl Package file with a few custom functions

So, you know the bare minimum about Mathematica Packages, and you know you should be using those new-fangled Paclet things, but you just want to get the absolute simplest autoloading of a .m or .wl Package file working.

Find your $UserBaseDirectory (just enter that on an input line to see). On a Mac it will be like:

/Users/username/Library/Mathematica

Under there you will find an Autoload folder. Choose an "application" name. (We're not in fact going to create a fully-fledged Application, just a mini one.) For this example we'll choose TestAuto. Make a folder of that name under Autoload:

$UserBaseDirectory/Autoload/TestAuto

Your code (we are "cheating" a bit here and not creating a full Application or Paclet) goes there. It can be a .m or .wl file. It needs a namespace within the application name, we'll choose `MyLib`, and place it in MyLib.wl

(* ::Package:: *)

BeginPackage["TestAuto`MyLib`"]

autoF::usage = "autoF[a,b] Does something with a and b (and will autoload)";

Begin["`Private`"]
autoF[a_,b_] := a^2 + b^2;
End[]
EndPackage[]

You need to create an additional folder Kernel and place an init.m file under it:

$UserBaseDirectory/Autoload/TestAuto/Kernel/init.m

You must pre-load your Package in that init.m file (this is an Autoload convention):

<< TestAuto`MyLib`

That's it. Restart Mathematica, and it will catch MyLib automatically. You can run your function immediately in a notebook without any additional namespace qualifier:

autoF[1,2]

5

You can also see that the Package is loaded by examining this (it might be quite long):

$Packages

...

You can list the functions in your library using this:

?"TestAuto`MyLib`*"

...

To learn how to create a fancier, more fledged Application, this David And Alice Park essay "A Mathematica Style" is a good place to start.