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I guess you could tell a fun story, but the students would learn nothing from it. You can't learn math without getting down to the details in a serious way. This is basically the pattern in Feynmann's book - it's all intuition and (almost) no detail. You can learn a lot of physics without getting your hands dirty too much (via informal thought experiments, easy calculations, etc). A book that tried to describe all of them would be just too disjointed and incoherent. At some point in your mathematical life, you will start to view them as one subject, but I don't think there is a way to teach undergraduates the foundational materials without having the topics fragment. Rather, there are an enormous number of topics (calculus, geometry, linear algebra, abstract algebra, topology, partial differential equations, combinatorics, probability, etc) each of which has its own pattern of thought. It's not that it is impossible for anyone to understand everything that is taught to undergrads - I certainly feel comfortable teaching any undergraduate-level course in my university. Math, even at the undergraduate level, is much bigger than physics. In fact, I don't think that such a book is possible. This should really be a comment, but I don't have the reputation.