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I mean, the very existence of magic kind of nullifies the concept of math as a means to ascertain objective fact.
What good is 2+2 when 2 eyes of newt plus 2 legs of frog leads to random quantities of dancing forks with literally no respect as to the how because magic?
Math can't quantify a world where physical laws are replaced by literal nonsense, and if math could ultimately explain the mechanics of magic and predict the outcomes of its applications, the magic wouldn't be magic anymore, it would just be another great force of the universe like gravity or electromagnetism to be mapped by the scientific community.
I think the one exception is their money, you definitely need some basic math to use it.
Exactly what more than 5th grade math do you need in such world?
I think a lot of people forget what they learn in 5th grade math. You learn negative numbers. You learn unit conversion, fraction, prime, square roots.
Would more math help absolutely. Especially with the logic wizard seems to lack. But it is not like many people use higher level math today anyway.
What they lack is knowledge about volume and surface calculation. That is some stuff you definitely need in life. That wizards don't need analysis or Calculus is kinda obvious.
For trivial calculations that’s still going to be accessible just by looking up a formula. For more complicated ones… I can’t remember the last time I needed something like that. What sorts of use cases are you thinking of?
I always wondered the opposite of the harry potter universe.
So much of math was difficult to teach or obscure because of difficulties in visualization or computation. Surely there would have been at least one wizard over hundreds of years that could figure out how to use the powers of illusion magic to visualize things? To demonstrate integrals to the unfamiliar? To render a fractal like a julia set?
Even if magic iteslf followed little internal logic, it could be used as a tool, surely? But that's the sort of fridge logic (warning tv tropes link) that maybe didn't belong in a story book like Harry Potter. I had to stop reading anyway around the time house elves were introduced, anyway. I took issue with that stuff even when I was a kid.
That's where arithmancy comes in.
I have often suspected that that's exactly what it is, there's even clues of a genetic basis. How such a force can somehow be responsive to specific language is hard to imagine but evidently it can.
There are laws baked into it, just like the formula proposed above. For whatever reason it's not only about intent, there are certain quantities of "stuff" needed. How is it that someone like Snape can map out such a specific spell, if it didn't take some sort of physical dynamics that could be measurable. Spells can't just solely be about intent, otherwise anyone could yell out "Cowabunga" or something and have it do whatever they are thinking. And I know some of the names have intent baked in them, but not all of them. Some are straight up nonsense. This doesn't even get into the fact that the wands are a straight up conduit to magic that are controlled more heavily than guns in most nations. Maybe the wizards just hide all the dragons, Phoenix and unicorns like nation states gaurd WMDs. It would be smart, without them most easy magic would be impossible and stuff would really take elbow grease with potions and whatnot.
If you haven't already, take a peek at Harry Potter and the Methods of Rationality. It's fanfiction, but absolutely worth a read.
Just a warning: this takes pretty much every bad FF trope you can think of and turns it to max. Awful reading.
I stopped reading it halfway through, and was too lazy to figure out why.
This explains it.
To add, the podcast is phenomenal. Definitely worth listening to as well
Oh man I totally forgot about that! Oh nice they have it in ebook and pdf formats now