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Nonanalytic Aspects of Mathematics and Their Implication for Research and Education

Philip J. Davis and James A. Anderson
SIAM Review
Vol. 21, No. 1 (Jan., 1979), pp. 112-127
Stable URL: http://www.jstor.org/stable/2029936
Page Count: 16
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Nonanalytic Aspects of Mathematics and Their Implication for Research and Education
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Abstract

In this paper we make a distinction between the practice of mathematics as it is usually presented--a logical chain of abstract, analytical reasoning from premises to conclusions--and how mathematics seems to be done in actuality--as a series of nonverbal, analog, often kinesthetic or visual insights. Mathematics in recent years has created a hierarchy with highly abstract, logical and symbolic material at the peak and with more geometrical, visual, and analog material held to be of lesser worth. We argue that humans are known to vary widely in their approaches to cognition and that the areas of the human brain specifically related to language and logical analysis seem to comprise only a part of the machinery of our intellect. We suggest that it would be wise for the practitioners of mathematics, and perhaps especially the students of mathematics to be aware of the very important nonverbal elements in mathematics. We feel that excessive emphasis on the abstract, analytic aspects of thought may have had deleterious effects on the profession and that a more appropriate balance, more in line with our cognitive endowment as humans, is desirable.

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