He spends much time on "minute" quantities at the start, but the explanation doesn't really make sense. To me, it's a mental model I can't trust, like rickety stairs.
The book is explicitly calculus-as-a-bag-of-tricks; monkey-see, monkey-do. As he says:
What one fool can do, another can.
(Ancient Simian Proverb.)
Fair enough on proofs. BTW in the free gutenburg edition (maybe MG differs): "prologue" doesn't mention proofs, but that textbook writers make it difficult (no "introduction" - also no "preface", except to the 2nd ed):
> The fools who write the textbooks of advanced mathematics ... seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.
Yeah, this sounds right. I think MG contextualizes it a little bit more. I actually like the book for the exercises and MG's footnotes especially, but as I worked through it I had to consult other resources to make sure I wasn't missing anything. The Khan Academy Youtube channel was very helpful for this.
The book is explicitly calculus-as-a-bag-of-tricks; monkey-see, monkey-do. As he says:
Fair enough on proofs. BTW in the free gutenburg edition (maybe MG differs): "prologue" doesn't mention proofs, but that textbook writers make it difficult (no "introduction" - also no "preface", except to the 2nd ed):> The fools who write the textbooks of advanced mathematics ... seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way.