The classical view of mathematics is essentially descriptive: we try to describe the facts about a static mathematical universe. Thus, for example, we report that every polynomial of odd degree has a root, and that there is a digit that occurs infinitely often in the decimal expansion of π. In opposition to this is the constructive view of mathematics, which focuses attention on the dynamic interaction of the individual with the mathematical universe; in the words of Hao Wang, it is a mathematics of doing, rather than a mathematics of being. The constructive mathematician must show how to construct a root of a polynomial of odd degree, and how to find a digit that occurs infinitely often in the decimal expansion of π.
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