Numerals first developed around 3100 B.C.E.
Numerals were created to keep records of commodities.
The numeral “18” developed from the sign for grain.
Accountants introduced unique numeral signs for use with signs for commodities.
[#paragraph1][#highlight1]Although literacy appeared independently in several parts of the prehistoric world, the earliest evidence of writing is the cuneiform Sumerian script on the clay tablets of ancient Mesopotamia, which, archaeological detective work has revealed, had its origins in the accounting practices of commercial activity.[/highlight1] Researchers demonstrated that preliterate people, to keep track of the goods they produced and exchanged, created a system of accounting using clay tokens as symbolic representations of their products. Over many thousands of years, the symbols evolved through several stages of abstraction until they became wedge-shaped (cuneiform) signs on clay tablets, recognizable as writing.
[#paragraph2]The original tokens (circa 8500 B.C.E.) were three-dimensional solid shapes—tiny spheres, cones, disks, and cylinders. A debt of six units of grain and eight head of livestock, for example, might have been represented by six conical and eight cylindrical tokens. To keep batches of tokens together, an innovation was introduced (circa 3250 B.C.E.) whereby they were sealed inside clay envelopes that could be broken open and counted when it came time for a debt to be repaid. But because the contents of the envelopes could easily be forgotten, two-dimensional representations of the three-dimensional tokens were impressed into the surface of the envelopes before they were sealed. Eventually, having two sets of equivalent symbols—the internal tokens and external markings—came to seem redundant, so the tokens were eliminated (circa 3250–3100 B.C.E.), and only solid clay tablets with two-dimensional symbols were retained. Over time, the symbols became more numerous, varied, and abstract and came to represent more than trade commodities, evolving eventually into cuneiform writing.
[#paragraph3]The evolution of the symbolism is reflected in the archaeological record first of all by the increasing complexity of the tokens themselves. The earliest tokens, dating from about 10,000 to 6,000 years ago, were of only the simplest geometric shapes. But about 3500 B.C.E., more complex tokens came into common usage, including many naturalistic forms shaped like miniature tools, furniture, fruit, and humans. The earlier, plain tokens were counters for agricultural products, whereas the complex ones stood for finished products, such as bread, oil, perfume, wool, and rope, and for items produced in workshops, such as metal, bracelets, types of cloth, garments, mats, pieces of furniture, tools, and a variety of stone and pottery vessels. The signs marked on clay tablets [#highlight6]likewise[/highlight6] evolved from simple wedges, circles, ovals, and triangles based on the plain tokens to pictographs derived from the complex tokens.
[#paragraph4]Before this evidence came to light, the inventors of writing were assumed by researchers to have been an intellectual elite. [#highlight7]Some[/highlight7], for example, hypothesized that writing emerged when members of the priestly caste agreed among themselves on written signs. But the association of the plain tokens with the first farmers and of the complex tokens with the first artisans—and the fact that the token-and-envelope accounting system [#highlight9]invariably[/highlight9] represented only small-scale transactions—testifies to the relatively modest social status of the creators of writing.
[#paragraph5]And not only of literacy, but numeracy (the representation of quantitative concepts) as well. The evidence of the tokens provides further confirmation that mathematics originated in people’s desire to keep records of flocks and other goods. Another immensely significant step occurred around 3100 B.C. E., when Sumerian accountants extended the token-based signs to include the first real numerals. [#insert1] Previously, units of grain had been represented by direct one-to-one correspondence—by repeating the token or symbol for a unit of grain the required number of times. [#insert2] The accountants, however, devised numeral signs distinct from commodity signs, so that eighteen units of grain could be indicated by preceding a single grain symbol with a symbol denoting “18.” [#insert3] Their invention of abstract numerals and abstract counting was one of the most revolutionary advances in the history of mathematics. [#insert4]
[#paragraph6]What was the social status of the anonymous accountants who produced this breakthrough? The immense volume of clay tablets [#highlight11]unearthed[/highlight11] in the ruins of the Sumerian temples where the accounts were kept suggests a social differentiation within the scribal class, with a virtual army of lower-ranking tabulators performing the monotonous job of tallying commodities. We can only speculate as to how high or low the inventors of true numerals were in the scribal hierarchy, but it stands to reason that this laborsaving innovation would have been the [#highlight12]brainchild[/highlight12] of the lower-ranking types whose drudgery it eased.