Chaitan
Chaitin describes in his book "Meta Math! The Quest for Omega" his point of view on information theory, complexity theory and a number of other questions (some of which should not be taken too serious, e.g. when he's comparing evolution and quantum physics). The whole book is dedicated to telling the story of how he discovered whta is now called Chaitin's constant and the theory connect with it by thinking about rather simple(looking) questions in computer sciences. (It is therefore a very unusual math book)
If someone is interested in how non-math-question can lead to new math, this book is definitely one of the places to find examples. You can find a online reader for the book here.
