Humanity’s primal (原始的) efforts to systematize the concepts of size, shapes, and number are usually regarded as the earliest mathematics. However, the concept of number and the counting process developed so long (67) the time of recorded history (there is archaeological (68) that counting was employed by humans as far back as 50,000 years ago) that the (69) of this development is largely conjectural (好推测的). Imaging how it probably came (70) is not difficult. The argument that humans, (71) in prehistoric times, had some number sense, at least (72) the extent of recognizing the concepts of more and less when some objects were (73) to or taken away from a small group, seems fair, for studies have shown that some animal possesses such a (74) . With the (75) evolution of society, counting became necessary. A tribe had to know how many members it had and how many enemies, and shepherd needed to know (76) the flock of sheep was decreasing in size. Probably the earliest way of keeping a count was by some tally (计算, 记录) method, (77) the principle of one-to-one corre-spondence. In (78) a count of sheep, for example, one finger per sheep could be (79) . Counts could also be (80) by scratches in the dirt or on a stone, by cutting notches in a piece of wood, or by tying knots in a string. (81) , perhaps later, an assortment of vocal (82) was developed as a word tally against the number of objects in, a small group. And (83) later, with the development of writing, a set of (84) was invented to stand for these numbers. Such an imagined development is (85) by reports of anthropologists in their studies of present-day societies that are (86) to be similar to those of early humans.