The Wonderful  Gift  of  Mathematics

This theoretical analysis addresses “the unreasonable effectiveness of mathematics in the natural sciences ” (Wigner, 1960). For example, how is it that ellipses—constructed by Greek geometers nearly two millennia before Kepler used them—provide such precise models for describing planetary motion? Historical models of gravity and planetary motion frame arguments on the nature of mathematics, particularly the characterization of mathematics as the objectification of action. This characterization helps explain the effectiveness of mathematics while distinguishing mathematics from other disciplines. “How can it be that mathematics, a product of human thought, independent of experience, is so admirably adapted to the objects of reality? ” Albert Einstein (p. 464, in Kline, 1959) By 200 BC, Greek mathematicians had constructed conic sections and investigated many of their properties. Beyond lines and circles, these constructions included parabolas, ellipses, and hyperbolas, which had no practical application at the time (Kline, 1959). How is it, then, that conic sections provided models for projectile and planetary motion two millennia later, and with uncanny precision? This is just one example of the “unreasonable effectiveness of mathematics in the natural sciences ” (Wigner, 1960), which has marveled scientists for centuries. Wigner attributed this unreasonable effectiveness to the empirical law of epistemology: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve ” (p. 8). In this paper, I argue that, although mathematics is a product of human thought, it is not independent of experience. The main purpose of the paper is to characterize mathematics Anderson Norton is an Associate Professor of mathematics education i