Letters to a Young Mathematician
Ian Stewart, Letters to a Young Mathematician (Basic Books, 2007)
Summary: A quick tour through the mathematical spectrum: pure mathematics vs. applied mathematics, Platonism vs. formalism, some history, and some tips.
Key Quote: “If math were a building, it would resemble a pyramid erected upside down. Built on a narrow base, the structure would tower into the clouds, each floor larger than the one below.” - p. 38
Bottom Line: You should read this book if you are a young (or older novice) mathematician.