Mathematical equivalent of Feynman's Lectures on Physics? I'm slowly reading through Feynman's Lectures on Physics and I find myself wondering, is there an analogous book (or books) for math?  By this, I mean a good approach to mathematics given through sweeping motions, appeals to intuition and an emphasis on modern perspectives over historical development.
What strikes me about Lectures on Physics is its conceptual orientation. It is easy to read in that I don't need a pen and paper at hand to work through details, but I also find it necessary to regularly stop and contemplate his ideas and examples. Content-wise, it is not at the level of a calculus book. My impression is that it covers much of what would constitute an undergraduate education in physics. Of course, finding a single book to cover an entire undergraduate mathematics curriculum is likely impossible!  I'm looking for the same style, not necessarily the comprehensiveness.

The Princeton Companion seems to me to be an attempt to achieve a similar mixture of depth, accuracy, content, motivation, and context. However, because math is a different kind of subject, this is a very different kind of book.
