On the shifting structure of mathematical paradigms
pp. 461-472
in: Rolf von Eckartsberg (ed), Metaphors of consciousness, Berlin, Springer, 1981Abstract
Mathematics. The word brings many images to mind: strange symbols, difficult problems, absent-minded professors. For the average man, however, the word first implies some type of computation problem. It may be finding areas or percentages or simply adding and subtracting, but the main impression is of some type of practical arithmetic problem. This viewpoint has a lot of historical legitimacy. The earliest written mathematical records that we have date from more than 5,000 years ago. For the overwhelmingly greater part of this time, the importance of mathematics (and indeed its very truth) was perceived as stemming from the fact that mathematics was one way of describing the nature of the real world. In other words, mathematical statements are true because they describe or agree with or predict our perceptions of the real world, and mathematics is important because it lets us make statements and predictions about the real world more easily than we might otherwise be able to do.