I've read this book. It's definitely one of the more interesting and readable maths texts out there. I wasn't exactly sure I'd use the methods. Working as a mechanical engineer I probably go straight to numerical methods, or approximate things even more crudely and approximately than a mathematician's 'rough' work. Though "replace a complicated function with a rectangle" definitely resonated. Overall the impression was that it was full of great techniques for mathematicians and scientists puzzling out every bit of meaning they can from a situation whose true features aren't yet known.
This is a good book. Also, any time this kind of book becomes available (be it a 100 year old one or a new one), it is worth looking into - great improvements in isnight and simplicity are possible above the "baseline" of US math education today.
So for example, I posit that the engineers or scientists you might admire from the 1950's didn't learn calculus or linear algebra the way you did.
Feynman learned calculus from the textbook "Calculus for the Practical Man".
I also quite liked https://ocw.mit.edu/courses/res-6-011-the-art-of-insight-in-...
Which is, I think, the successor and quite useful.
Book PDF is here: https://direct.mit.edu/books/oa-monograph-pdf/2284035/book_9...
what is it about?
how to distribute fighters so that your team defeats-in-detail your opponents?
It is about useful tricks you can usually not learn in university classes.