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1 General

Wikipedia's Mathematics article describes the topic, not only its branches, but also how it is related to science, what the role of esthetics is in it, etc.

Paul Taylor: Practical Foundations of Mathematics. Free online book on mathematics, huge areas of mathematics are described thoroughly, many of them closely related to computer science and functional programming (relational algebra, category theory, Curry-Howard isomorphism).

G.J. Chaitin especially his Understandable Papers on Incompleteness, especially The Unknowable (the book is available on this page, just roll the page below that big colored photo). The book begins with the limits of mathematics: Cantor on pradoxes, Gödel on incompleteness, Turing on uncomputability, Chaitin on randomness); but (or exactly that's why?) it ends with writing on the future and beauty of science.

2 Topics