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Greek mathematics, especially the proof method of Euclidean geometry, provided the base to Western rationalistic thought; and the whole mathematical system, including Euclidean geometry, analytic geometry, calculus, probability theory, set theory and etc., laid the foundation of modern science. Mathematics is not only tools used in business, engineering, sailing, construction and other human activities, but also provides reasonable and rigorous structure for scientific discoveries and theory researches, and even determines the content and research methods of philosophy and creates many styles of painting, music and architecture...... By twentieth Century, mathematics has become a obligatory course in primary and secondary schools. When mathematics becomes one of essential education content, educators, mathematicians and the related administrators start to think a question: what mathematics is. Only by solving this problem, we will know the solution of "how to teach mathematics ".

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