Mathematics How Mathematics Grows: The Term Paper

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Mathematics as the reading suggests posses many characteristics, being derived from individual genius but thriving only when the culture or wider community as described by the text accepts the principles and applications surrounding it (p. 64). Individual discovery alone however, is not responsible for mathematics. The text also notes that economic and social forces can stimulate mathematical discovery. Mathematical discovery however, is something that persists regardless of the historical time or culture dominating. The text notes that many theorists favor the "doctrine of culture" so one must acknowledge the influence culture has on discovery. The text suggests the dichotomy between the individual and the doctrine of the culture is false, an argument similar to that of mind over matter; one can conclude simply that individuals may matter temporarily but culture dominates the field of mathematics over wider time periods.

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That culture is inextricably linked to mathematical inquiry is a fact that can't be denied (Saxe, 1991). Wang (1963) notes that it is important however, to distinguish between mathematical discipline and application, suggesting that axioms may not be true in the physical world, and that individuals may influence mathematical possibility as much as culture. He notes Euclid's fifth postulate which was found later to be false, which Pasch (1882) pointed out when confirming the shortcomings in this once accepted axiomatization (Wang, 1963, p.2). Euclid's axioms were at first however, regarded as completed logical and necessary. However as times changed, especially during the Renaissance for example, controversy existed over the axiom and axiomatic systems in particular, giving rise to questions regarding the legitimacy of the axioms formulated by Euclid (Wang, 1963)......

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