I have no idea what you're talking about.Of course, wizards don't actually follow any of the paths you described traditionally.

I have no idea what you're talking about.Of course, wizards don't actually follow any of the paths you described traditionally.
Well presumably it's in the vicinity of what actual mediaeval people believed were the actual results of the prayers, magic etc being performed by real-life hermits, priests, miracle-workers etc.If that works for you. Seems a little too "clap your hands if you believe" to me though.
Nothing is being "dodged". It's a way to reconcile magic with the faux-mediaeval: assume a baseline in which magic is a necessary condition of the faux-mediaeval emerging and enduring.It seems like a way to dodge the issue, since it doesn't require changing anything.
Mediaeval farmers, builders, etc did not use mathematics. They used folk knowledge and techniques.I base this on pre computers people HAD to know math... every farmer every builder every smith uses math
Learning some math or physics does not a mathematician or physicist make. What you are describing with the person learning some math is a person who took the magic initiate feat and got a few cantrips. That's not a spellcaster. Spellcasters have a PhD in spellcasting.3) My point has always been, and remains, that the floor for learning to cast spells cannot rationally be the heights of professional advancement, but the practical usage of working people, even if only those at the higher end of the journeyman’s skill and knowledge. This is why “how many mathematicians in Europe” is not a question I see any value in the answer to. It doesn’t tell us anything we cannot glean from the effect of mathematics on crafts, architecture, economics, astronomy, chemistry, and whatever else, over many generations, because one needn’t be Newton to use mathematics or even to learn advanced mathematics like calculus and apply it to solutions to practical problems.
It does. You have to change the lore of the world. Suddenly the world is vulnerable to disruption(locally and globally) of the hard work it is taking to keep things just okay.It seems like a way to dodge the issue, since it doesn't require changing anything.
Knowing some basic math =/= mathematician, though.my guess (and I am no historian so this is pull out my backside numbers) between 25% and 50%.
I base this on pre computers people HAD to know math... every farmer every builder every smith uses math
And probably an editor.Surely if we're counting folks able to do some arithmetic as mathematicians, then you know enough history for us to count you as a historian. Having successfully put thoughts onto (virtual) paper it feels like you should also be open to claiming credit as a writer. ;-)
Knowing basic arithmetic doesn't make you a mathematician. I know basic maths but I wouldn't, nor would anyone else, call me a mathematician.my guess (and I am no historian so this is pull out my backside numbers) between 25% and 50%.
I base this on pre computers people HAD to know math... every farmer every builder every smith uses math