This book is fantastic! It's Spivak so it doesn't sacrifice prose for precision, and it does more than teach physics from a mathematical point of view. It also illustrates the massive gap between theoretical physics and experimental physics-- why physics is so hard. An early example in the book is trying to calculate the way a chain hanging off an edge falls: Several pages of investigation reveal how devilishly hard it is to apply the theory to a particular problem-- even demonstrating that a popular physics book gets the problem wrong and the best guide for how to analyze it correctly is experiment.

I hope there's a sequel!