This work develops and defends a structural view of the nature of mathematics,
which is used to explain a number of striking features of mathematics
that have puzzled philosophers for centuries. It rejects the most widely
held philosophical view of mathematics (Platonism), according to which
mathematics is a science dealing with mathematical objects such as sets and
numbers—objects which are believed not to exist in the physical world.
Often we mathematicians are inarticulate when challenged to explain
why mathematics is such a critical aspect of K - 12 education today. We
know it is, but are so involved in the subject that we have not looked at
the broader perspective of the way in which mathematics actually interacts
with today’s society. So what follows are some observations that may well
be useful in this regard.
“The study of economics does not seem to require any specialized gifts of an
unusually high order. Is it not, intellectually regarded, a very easy subject
compared with the higher branches of philosophy or pure science? Yet good, or
even competent, economists are the rarest of birds. An easy subject, at which few
excel! The paradox finds its explanation, perhaps, in that the master-economist
must possess a rare combination of gifts. He must reach a high standard in several
different directions and must combine talents not often found together.