alt Hacker News> Waiting a year to get from intuition to theorems is a perfect way to ruin math.
It's interesting that you chose to make that point in a thread about calculus specifically. It had pretty shaky foundations for most of its history, and even today, there's a pretty significant disconnect between the mechanics of epsilon-delta and the meaning we assign to the result.
> Math is not supposed to be easy/simple, but it supposed to be a great way to understand systems based thinking.
Math is a means to an end. Making the tool easy to use is a desirable property. I've heard "it's not supposed to be easy" applied to many disciplines, from film photography to software engineering, and I think it's mostly gatekeeping.
> even today, there's a pretty significant disconnect between the mechanics of epsilon-delta and the meaning we assign to the result.
I think this is practically fixed by Robinson's NSA when it's combined with big/little O notation:
A (nonstandard real) quantity is o(δx) when it's infinitesimal relative to δx, i.e. s ∈ o(δx) whenever s/δx is infinitesimal. So δx² ∈ o(δx) but δx ∉ o(δx).