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. 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.

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.


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 likewise evolved from simple wedges, circles, ovals, and triangles based on the plain tokens to pictographs derived from the complex tokens.

Before this evidence came to light, the inventors of writing were assumed by researchers to have been an intellectual elite. Some, 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 invariably represented only small-scale transactions—testifies to the relatively modest social status of the creators of writing.

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. 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. 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.” Their invention of abstract numerals and abstract counting was one of the most revolutionary advances in the history of mathematics.

What was the social status of the anonymous accountants who produced this breakthrough? The immense volume of clay tablets unearthed 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 brainchild of the lower-ranking types whose drudgery it eased.

虽然读写能力在史前世界几个区域独立出现，最早的文字证据是在古代美索不达米亚黏土碑发现的楔形苏美尔笔迹，地质勘探结果表明文字来源于商业活动的计数实践。研究者证实，没有读写能力的人为了记录他们生产和交换的货物用黏土符号创造了一个计数系统作为他们产品的象征性代表。经历了几千年，这些符号经历几个抽象阶段的进化，直到他们成为在黏土碑上楔形的符号，即可辨认的文字。 原始的符号（大约公元前8500年）是三维的固定的形状-小球形，圆锥形，圆盘形和圆柱形。例如，六个单位的谷物和八头牲畜的账可能是被六个圆锥形符号和八个圆柱形符号代表。为了把一堆符号聚集在一起，有所创新（大约公元前3250年），这里符号被封存在黏土信封中，当还债的时候可以敲碎打开并且计数。但是因为信封的内容可以轻易被遗忘，在他们被封存之前，三维符号的二维代表被刻在信封的表面。最终，有两套对等的符号-内部符号和外部痕迹-这看起来累赘，所以符号被消除（大约公元前3250-3100年），只有带有二维符号的黏土碑被保留。随着时间的推移，符号变得越来越多，丰富，抽象，并且代表了除贸易货物以外更多的含义，最终进化成楔形文字。 符号的进化在地质记录里有所反映，首先是因为符号本身越来越复杂的性质。最早的符号要追溯到大约10，000到6000年前，仅仅是最简单的几何形状。但是大约公元前3500年，更复杂的符号开始广泛使用，包括许多自然的形状如小型工具，家具，水果和人类。更早的简单的符号是农产品的计数，然而复杂的符号代表成品，像面包，油，香水，羊毛和绳子，还有在车间生产的产品，比如金属，手镯，布料的种类，衣服，垫子，家具，工具和多种石制与陶制的容器。类似的，在黏土碑上刻的记号同样由简单的楔形，圆形，椭圆形和三角形演化而来，基于从简单符号到来源于复杂符号的图片文字的变化。 在证据为人所知之前，研究者认为文字发明者是有智慧的精英。比如，有些人假设文字出现于神职人员阶层内部约定的文字符号。但是简单的符号和最早的农民的联系，复杂符号和最早的工匠的联系，还有符号信封计数系统总是仅代表小规模交易的事实-证实了文字创造者相对卑微的社会地位。 不仅仅是读写能力，还有计算能力（量概念的表示）。符号证据进一步证实数学来源于人们记录家禽和其他商品数目的愿望。另一个具有重大意义的进展发生在大约公元前3100年，这时苏美尔人扩展基于符号的标记直到第一个真正的数字。以前，谷物单位被一对一对应-表现为需要的谷物单位的重复符号或标志。然而，会计们设计出与货物标记不一样的数字标记，这样十八个谷物单位都可以通过一个谷物标志和一个表示十八的符号表示。抽象数字的发明和抽象计数是数学史上最具有革命性的进步。 这些创造出重大突破的匿名会计们的社会地位怎么样？在苏美尔庙宇遗迹中出土的大量黏土碑上保存的记录表明抄写阶层的社会分级，有大批低阶层的制表人都在做单调的计数商品工作。我们只能推测数字发明者在抄写阶级的地位高低，但是我们有理由推测这种节省劳动力的创新可能是低等级阶层为缓解劳苦的点子。