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> 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.

by ogogmad2 hours ago|

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> 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:

  δy = f'(x) δx + o(δx)

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).