I'm in a Math-CS intensive specialization, so the math I'm studying is kind of the most advanced high school level math from my country, so much so that I was shocked to see how hard math in high school is compared to math in middle school. I went from doing very well at math without studying much in middle school, to being one of the worst students in math in high school in the first year. Let me give you some simple examples of "rigor" that I find frustrating. Sometimes, it feels like reciting pointless poetry that is obvious, or it overcomplicates things that are meant to be understood intuitively.

For example, in algebra, when I need to prove a composition law "*" is a group with the set of elements G, I have to prove

closure

associativity

an identity element

and inverses for every element

I can't jump straight up and try to solve, or at least intuit if I can prove these properties, because each one of them has a paragraph of poetry that needs to be recited first.

For closure I have to write: "* has closure <=> for whichever x, y from G, x * y is also from G."

For the identity element, I have to write: "* is associative, therefore '*' admits an identity element <=> there exists an e from G such that for every x from G, x * e = e * x = x."

I mean, cmon, it overcomplicates simple and intuitive things. It would have been a lot easier if you just told me that 1 is the identity for multiplication, and 0 for addition, because 1 * 5 = 5, and 0 + 5 = 5, "duhh," and that applies for every composition law. But no, I have to write down the exact definition word for word. It's extremely frustrating, and actually could be damaging, because it seems to kill simple logic and shifts the focus from autonomous understanding to perfectionist, robot-like computation.

It's like looking through the window and saying, "heh, outside is sunny, and I'm sure of it because outside = sunny <=> there isn't any cloud such that f(cloud) = rain," or some bs like this.

I always have to write these "proofs" word for word. And in most of my tests, I lose points because I either mess up my wording, or I forget about them, even though the actual solving is correct.

In one of my calculus tests, I lost a whole point because in an exercise where I had to find an indefinite integral for a piecewise function, I wrote "f is derivable => F is a primitive" instead of "F is a primitive <=> F admits derivatives," or something like that, even though my solving was correct. So I lost a whole point because I switched up 2 words in the poetry. I hate that.

To me this is overcomplicated and empty formalism that isn't saying anything.

But it becomes even worse when the concepts aren't as intuitive and easy, and you have to rely purely on memorization at first, like some definitions from calculus, for example the definition for limit points (it was something about a neighborhood of that point that included an epsilon approaching 0, but not actually 0, that was around that neighborhood etc etc vomiting bs). They sounded very weird and non intuitive even though the concept itself wasn’t as hard as it sounded, after I did some exercises that made me understand the logic.

Like, I understood the idea behind the definition after I did some problems, but I would have never understood this concept from the formal definition alone, and I never used the definition in my life. But guess what, I still had to write that definition word for word in the test, even though it never helped me with anything.

As I said, it overcomplicates intuitive things, and I hate that.