But what does that mean when you take out the math?
Well, that question has perplexed me for months. This post was supposed to go out with the rest of the "without Math" posts. Clearly, it did not...
Because I can't really say what a math-less magic-user would look like. It has a kind of backwards quality about it that the other classes do not. Every fighter can do the same things, as far as the game is concerned. The details about how they do it, i.e. what weapons they use, how much armor they wear, whether they focus on Dexterity or Strength...none of it really matters. They are still a fighter because they do fighter stuff. Hit things with weapons, absorb some damage, protect the less combative party members, run into the danger.
But...what is magic-user stuff? Fireball? Magic missile? Scribe Scroll? Reading magic? There is an argument to be made that, yes, that is magic-user stuff. If you can do those things, you are a wizard. But not every magic-user ever learns magic missile or fireball, or how to scribe scrolls, or even how to read magic. As more and more spells are printed, and the boundaries of what magic can and cannot do (and how easily it can or cannot do it) has expanded, we have found that very specific types of casters are now viable. Casters that don't use spellbooks. Casters that even change the very idea of how mortals can access magic.
Also, "fireball" and "protecting the squishy guys" are not the same level of abstraction. "Fireball" would be better described as "AoE damage." "Magic Missile" is best described as "unavoidable magic damage that's cheap." Of the four core classes, none but the magic-user can do those things. But is an illusionist, who knows no damaging spells at all, a magic-user then?
Must we abstract further and higher? Maybe the magic-user is the class that makes sweeping changes to the environment the party is in, either clearing obstructions or creating them. This definition would then include things like knock and illusory terrain, which are yet more staples of the D&D wizard. Looking over the wizard spell list from 3.5, I think this definition is rather complete. But it is so general that it could take any in-game form whatsoever. Wizard, sorcerer, illusionist, evoker, swordmage, abjurer, warlock...even divine casters could fit within this definition comfortably.
And yet, this definition leaves us with nothing but "casts spell" as the 'math-less' portion of a magic-user. Essentially, we're back where we started.
We don't want to have to write up all these different classes, because we would never be done. If we want to be able to write up a coherent set of rules for all magic-users (math-free, of course), we have two options:
1. Make it wizards only. If you can cast arcane spells without a spellbook, it's because you are a monster or demon or dragon and not a PC. Humanoid races have only one way to learn and use magic, and that's spells and spellbooks. If you take D&D as written, remove every non-wizard arcane casting class, you have this system. There is still a lot of room here. Every type of wizard specialist is available. Spell selection is wide open and creates meaningful differences between all wizards.
2. Make it up as it becomes relevant. Have no written rules in your system for spells and magic. Instead, make magic entirely an in-game discovery and learning process. If you want to have the PCs fight a dark mage, write up the basics of how that guy knows/can use magic. This could be any micro-system of your choosing. The most obvious is a spellbook with a finite number of spells. What system you use to prevent characters from casting these spells endlessly each day is up to you. Then, if the PCs decide to investigate this dude's magic (presumably after turning him into a fresh corpse), they can pursue it, and you'll know exactly how it works and how powerful it is.