Out of the Labyrinth by Robert Kaplan

Author:Robert Kaplan
Language: eng
Format: epub
Publisher: Bloomsbury Publishing
Published: 2013-03-10T16:00:00+00:00

The “math is discovered”/“math is invented” dichotomy used to be innocent, the latter view naturally accompanying times of great mathematical ferment, the former, times of consolidation—and both leaving their traces in the teaching that scrambled to keep up. Now this opposition has been co-opted by rather boring political factions. Conservatives need an intellectual fixed point: God may no longer exist, but Math is still omniscient. Even if you never understood it—perhaps especially if you never understood it—it has the comforting status of divine absolutism. If the social world is in terrifying flux and morality has lost its bearings, at least Math is fixed and unambiguous.

The New Right of 1985 called what was then the New Math (investigation, problem-solving) “the latest stage in a disastrous process that has seen school mathematics drift toward becoming a low-level empirical science.” The New Left sees in math an easy and early opportunity to make independent discoveries, untrammelled by the immense data-gathering needed in other fields—but then, ashamed of its elitist past, would put all mathematical ideas, however misguided, on a Politically Correct par, where sincerity displaces rigor as the touchstone, and such lurid flora as Ethnomathematics sprout. It is just common sense, of course, to take into account the context of life and thought in, for example, ancient India, when studying the rise of number theory there; or the Greek context, when looking at how geometry and deductive proof arose in its midst. The silliness starts with claims that mathematics follows from rather than underlies cultural phenomena; that rather than being universal it is fundamentally different in its Eastern and Western varieties, and speciates with national differences; and that one can only fully understand and enjoy the mathematics of one’s physical rather than spiritual ancestors. Here too you will find that recently fashionable reinterpretation of Karl Popper’s “falsifiability” criterion as a desirable end: mathematics should be in perpetual revolution, with any hint of its having unearthed a morsel of Being discarded as antiquarian thinking. So Right and Left misread as centrifugal or centripetal the rising spiral of abstract recursion.

Is mathematics the material of thought or a way of thinking? The first hardly differentiates it from the other sciences, taking it as “out there,” to be discovered. Mathematics as a way of thinking received its greatest impetus from those Formalists who sought to logicize mathematics, giving logic and math alike the common language of set theory. They rode high, as far as teaching went, in the 1970s, with that New Math, which left parents unable to help their offspring decode Venn Diagrams, and teachers at a loss to decide which solution sets were complete (though it was rather fun rolling the Well-Formed-Formula dice, and filling in truth tables).

Which is the proper clientele of the mathematical enterprise? Lancelot Hogben’s 1937 Mathematics for the Million wasn’t the first attempt at popularization. For that you have to go back at least as far as AD 100 and the Introductio Arithmetica of Nichomachus of Gerasa, which entertained schoolchildren for a thousand years with its numbers dressed up as fanciful animals.

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