Which poses the question: What Maths correspond to what Wind? Some thoughts:
Ulgu is fuzzy logic, because that's very concerned with truth and blurring the line.
Hysh is regular logic, where truth is an absolute and things are pure. And if you convert something to conjunctive normal form, you can have a ton of people with very little knowledge evaluate the subclauses.
I can't really think of any goods ones for the rest.
No neat mapping/divisions I think. Some Winds have very little to do with math at all. Ulgu works a lot with probabilistics though, taking uncertainties to extract information
I think you are wrong and you are implicitly contradicting word of god.
If the end result of spell creation is a compiled 'spell' then grey college knowledge wasnt increased, if a paper were written about the process of creating that spell you might increase the techniques available and advance their knowledge/skill base but from everything weve been told magic is to personal for that to happen.
Spell creation grants new tools in a use case sense but absolutely not in a technique/knowledge base sense. At least for any one other than the person that created the spell.
Theres a big difference between inventing a spell or magical process you can cast, and developing a spell that people can be taught.
The latter is an increase to College knowledge(though the value of the increase is debatable), the former is increasing your personal abilities.
As had been described to us thus far, the spell development process tends to go thus:
1) Personal quality of some form, whether its a trait, particularly in depth insight, arcane mark or even a spell mastery.
2) Inspiration or motivation intersecting with the above quality.
3) Developing the spell itself.
4) Making the spell comprehensible to people with some of your set of traits.
5) Making the spell comprehensible to people who only share a Wind.
6) Making the spell comprehensible to people who use different Winds.
If you make it to 4, you have a neat trick you could teach a personal apprentice, but would not add to the College's lore significantly, you'd have to basically teach your trait(which we know can be done, but not easily or completely, we did it with Waaaghbane).
If you make it to 5, you have separated casting the spell with the state of being the spell's inventor. The spell has been isolated from the insights that leads to the specific mental state and Wind combination that produces the spell.
Thus, learning spells taught at a stage 5 and above level is relatively safe, easy and fast, but in exchange the only immediate gains are what you would have achieved from expanding your spellbook, the Magic score increases or eventually the Loremaster trait.
On the other hand, having a new spell does mean you can crit with the spell and develop a trait, or abuse the shit out of the spell and develop a trait that way.
To extend the compiled code metaphor further, it's however possible (if you know what you're doing) to disassemble the package and look under the hood. Just don't try to do it in the first few months after learning how to program.
You'll just go crosseyed/blow something up. We're missing a trait to be able to get the insight that Melkoth has.
That's like trying to look under the hood of CPython, but not knowing enough C. Or knowing just enough C to read the code and write your own toy project, but not enough to handle code of that complexity yet. (Yes, i'm speaking from experience ;P)
Having handled decompiled code before, you basically learn shit all about how the code actually works, and are usually better off just creating your own version of that code using the decompilation as an unguided tour through the logic.
. High level maths makess my head hurt
