As far as I've understood so far, back when calculus was invented people would think about it using infinitesimals. But nowadays it is taught without mentioning them; in short, caluclus is now taught emphasizing the ability to use the techniques and that's it.
I think that during the 19th century when it (along with logic) was being formalized they decided to throw away the old original ways to think about it. This ends up making it really hard to understand in exchange for making it "formally sound" and "user friendly".
I think that during the 19th century when it (along with logic) was being formalized they decided to throw away the old original ways to think about it. This ends up making it really hard to understand in exchange for making it "formally sound" and "user friendly".