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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Philosophy of mathematics Introduction to Mathematical Philosophy, Irrational number, Valuation (logic), Logicism, Formalism (mathematics), Intuitionism, Constructivism (mathematics), Fictionalism, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Applied mathematics, A Mathematician's Apology, Foundations of mathematics, Mathematical logic, Mathematical proof