That's a lot of definitive statements for something as poorly defined as "art".

>The question to ask with art is a simple one: when people saw it, did it make them feel or think differently are the moment? And did it make them feel differently from the way other art pieces did?

Why? Why is that the question to ask? Why must be considered in this specific way, rather than any other?

>You can't understand art without understanding the audience, because art is made for the audience

So something that's made to be made rather than to be seen is not art, even in the case that if someone did see it they would think it's art?

>You can't examine art in itself, just like you can't examine a mechanical tool in itself, without asking why it was made, what it was made for, and whether it was good in doing that.

No. No, no, no. There's no justification for this besides that you say so. Why can't I look at the thing in isolation and decide for myself what it's good for? What do I care what the person who made the wood saw thought he was making? If for my purposes it's a good screwdriver and I use it like that, is it wrong because I'm not properly interpreting the message the manufacturer embedded into the tool?

>You can't look at art and discuss its merits without understanding how it transforms people it's shown to (and what audience the art was meant for). You need to tell early 20th century suprematist art apart from art made today, and you need to know whether it actually could make people in early 20th century feel and think differently in response to it to talk about the art's merits.

Again, why? Exactly what prevents me from doing that? What, I'm barging into a club? Well, sorry, but I didn't see any signs on the door. I just saw a bunch of people gushing over trash and thought I'd speak my mind. If you don't like that I don't like what you like because I don't care about the things you care about then that's too bad.

>the same criteria apply to mathematics, which is art with a particular audience in mind. Anyone can prove the Pythagorean theorem, and many have rediscovered it. It would be asinine to say it has no mathematical merit, or that Pythagoras wasn't a great mathematician.

Interesting line of reasoning. Mathematics is art, therefore mathematical merit is artistic merit. Artistic merit by my definition is about originality, therefore mathematical merit (being artistic) is about originality. I hope I don't need to say I don't agree with either the soundness of the reasoning nor with the conclusion.

I don't agree that mathematics is art with no qualifiers whatsoever. Mathematics is, very reductively, primarily concerned with the search for true statements, not with the search for beautiful statements, nor with self-expression or cultural transmission.

>But you'd have no idea what's so important about Calculus if that was all you knew about it - which, sadly, is how it's taught, and which is why people have no appreciation of neither mathematics, nor art.

Calculus is useful, regardless of its history. The reason people don't appreciate mathematics is because a) they think mathematics is manually calculating things (because that's what they're taught to do), which sours them to the idea, and b) they're forced to learn things they think has nothing to do with their daily lives, not because they don't learn about the history. And if we're honest, they're right. Very few people will ever need to know calculus at any point in their lives (outside of school), and fewer still will need to calculate things by hand.

>You'd need to know how mathematics was before calculus, what compelled people to develop it, how it affected mathematicians, what kind of mathematics came into existence because of it, and ultimately, how it changed the world.

That's one way to appreciate it, I'm not denying that. But you're arguing that it's the way to appreciate art, and that if I don't do that I'm missing the point.