In reading The cultural niche: Why social learning is essential for human adaptation in PNAS I couldn’t help but think back to a conversation I had with a few old friends in Evanston in 2003. They were graduate students in mathematics at Northwestern, and at one point one of them expressed some serious frustration at the fact that so many of the science and business students in his introductory calculus courses simply wanted to “learn” a disparate set of techniques, rather than understand calculus. The reality of course is that the vast majority of people who ever encounter calculus aim to learn it for reasons of utility, not so that they can grok the fundamental theorem of calculus. With the proliferation of tools such as Mathematica and powerful portable calculators fewer and fewer people are getting their hands dirty with calculus in an analytic sense, and more often see it as simply a “requirement” which they have to pass.
Calculus, and mathematics generally, is a clean and crisp human invention. In the late 17th century Isaac Newton and Gottfried Leibniz originated calculus as we understand it. Later thinkers extended their work. But for the vast majority of humans who have ever learned calculus it is simply a “black box” set of techniques which work rather magically. They did not contribute anything new to the body of knowledge which they drew upon. Mathematics is part of our cultural patrimony, we implicitly stand upon the shoulders of giants without apology. Such is to be human.
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