Watch a baby between six and nine
months old, and you will observe the basic concepts of geometry being learned.
Once the baby has mastered the idea that space is three-dimensional, it reaches
out and begins grasping various kinds of objects. It is then, from perhaps nine
to fifteen months, that the concepts of sets and numbers are formed. So far, so
good. But now an ominous development takes place. The nerve fibers in the brain
insulate themselves in such a way that the baby begins to hear sounds very
precisely. Soon it picks up language, and it is then brought into direct
communication with adults. From this point on, it is usually downhill all the
way for mathematics, because the child now becomes exposed to all the nonsense
words and beliefs of the community into which it has been so unfortunate as to
have been born. Nature, having done very well by the child to this point, having
permitted it the luxury of thinking for itself for eighteen months, now abandons
it to the arbitrary conventions and beliefs of society. But at least the child
knows something of geometry and numbers, and it will always retain some memory
of the early halcyon days, no matter what vicissitudes it may suffer later on.
The main reservoir of mathematical talent in any society is thus possessed by
children who are about two years old, children who have just learned to speak
fluently.