Reading Stephen Wolfram below suggests why mathematical reasoning, at least the greatly creative kind, is unteachable:
Of the limited set of people exposed to higher mathematics, different ones often seem to think in bizarrely different ways. Some think symbolically, presumably applying linguistic capabilities to algebraic or other representations. Some think more visually, using mechanical experience or visual memory. Others seem to think in terms of abstract patterns, perhaps sometimes with implicit analogies to musical harmony. And still others –- including some of the purest mathematicians -– seem to think distinctly in terms of constraints, perhaps using some kind of abstraction of everyday geometrical reasoning.
(Quoted from page 1177 of A New Kind of Science, by Stephen Wolfram. Wolfram Media, 2002.)
For a brief biography of Stephen Wolfram, click here. For images of or relating to Stephen Wolfram, click here.
Comments