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• Fields of mathematics

Mathematics is the science that deals with the measurement, properties, and relationships of quantities, as expressed in either numbers or symbols. For example, a farmer might decide to fence in a field and plant oats there. He would have to use mathematics to measure the size of the field, to calculate the amount of fencing needed for the field, to determine how much seed he would have to buy, and to compute the cost of that seed. Mathematics is an essential part of every aspect of life—from determining the correct tip to leave for a waiter to calculating the speed of a space probe as it leaves Earth's atmosphere.

Mathematics undoubtedly began as an entirely practical activity—measuring fields, determining the volume of liquids, counting out coins, and the like. During the golden era of Greek science, between about the sixth and third centuries B.C.,...