How come that high school math is full of this stuff, like doing manual matrix multiplications over and over, but not a single mathematical proof?
Society would really benefit from people training logical reasoning, which is what a mathematical proof is. Rather that than a manual matrix multiplication.
Heck, even most of my SWE colleagues can't even write down a real proof.
I love Math and this is sort of casual gaming.
Mathematicians and people who are/were good at math are always quick to disregard the "boring" math.
First I'd like so make it clear that I agree with you.
However, in reality, all this stuff is seen as a prerequisite to get to "the good stuff". Real world education systems have this gatekeeper in place for everyone who isn't exceptional.
So while I absolutely share your sentiment, I find it very misplaced (and a bit distasteful) here for a tool that can actually just help real world self learners overcome those barriers. Self learners that just want to learn the basics from ground up are already often ignored by the whole math community.
Math is exercising, that is something high school math and university math very much have in common.
Had OP posted a generator for proof based exercises and problems, I guarantee you some mathematician would've showed up to rant just as much about how trivial undergraduate level proofs are ;)
Yes, proofs are a powerful part of mathematics, but they aren't at all the only goal. For someone like a machinist, proofs seem entirely impractical and like a waste of effort. My high school geometry class was heavily proof based, and most of the people in my class couldn't understand why we were doing these exercises. As a result, they didn't actually learn many of the helpful tricks from intro geometry that can help with things like machining or carpentry. In fact, I'd talked to someone who was in that class that now runs a cabinetmaking shop and they mentioned feeling cheated in high school due to our geometry class. I thought it was very well taught, but I ended up doing a BS in math. I was surprised that we ended up with very different views of the same class >10 years later.
Plus, even after MS level math courses, I can appreciate the need to do exercises. I look at them the same way as practicing playing an instrument. Sure, you can intellectually understand everything about a performance, but the only way to learn is through practice. I haven't had to touch 3d calc in a hot minute, but an upcoming side project will need that. First thing I am doing is (legally acquiring) some undergrad textbooks and solution guides and working through problems before comparing results. Yes, I can do proofs, but going through a worked example and comparing results is an excellent way of learning.
Ultimately, they are.
I think these short outburst of calculations are helpful and fun. I for example host a private website for sub/add/mult/div tasks and consider them as same sort of casual gaming, solving these "math problems" in the shortest time possible.
Author's great repo inspired me to add more stuff. I like it.
And that's my criticism. If more people in society cared why something is true, we wouldn't have falsehoods abound all around us that are obviously wrong and logically screamingly incorrect.
Matrix multiplication is an uninportant detail. Modus ponens is what holds everything together. But rarely anybody can handle the latter, nor even has heard of it.
I might poke around with this and Anki sometime though and see if I was onto something!
Edit: The reason I ask is that providing a tex generator would possibly help K12 teachers generate exercise sheets, since obviously the terminal output wouldn't do for providing to students. I see that basic Tex is availiable, but from what I see it doesn't support templates.
I'd love to get some input on this.