> My understanding is that they are part of nature.  If you think about it, to hunter-gatherer-level societies, negative numbers could be called "imaginary":  There is no such thing as "negative-3 sheep", for instance.  Nor is there a third of a (living) sheep.  It was easy enough for people to divorce themselves from the idea of integers, or positive numbers.  It was much more difficult to deal with "irrational numbers" (numbers which could not be expressed as the ratio of two integers).