History of ancient numeral systems

[8] Possible tally marks made by carving notches in wood, bone, and stone appear in the archaeological record at least forty thousand years ago.

[12] Similar artifacts from contemporary societies, like those of Australia, also suggest that such notches can serve mnemonic or conventional functions, rather than meaning numbers.

[14] Noting the statistical probability of producing such numbers by accident, researchers like Jean de Heinzelin have suggested that the notch groupings indicate a mathematical understanding far beyond simple counting.

It has also been suggested that the marks might have been made for a utilitarian purpose, like creating a better grip for the handle, or for some other non-mathematical reason.

[15] The earliest known writing for record keeping emerged from a system of accounting that used small clay tokens.

The earliest artifacts claimed to be tokens are from Tell Abu Hureyra, a site in the Upper Euphrates valley in Syria dated to the 10th millennium BCE,[16] and Ganj-i-Dareh Tepe, a site in the Zagros region of Iran dated to the 9th millennium BCE.

Tokens of different sizes and shapes were used to record higher groups of ten or six in a sexagesimal number system.

This process created external impressions on bullae surfaces that corresponded to the enclosed tokens in their sizes, shapes, and quantities.

The correspondences between impressions and tokens, and the chronology of forms they comprised, were initially noticed and published by scholars like Piere Amiet.

[20][21][22][23] By the time that the numerical impressions provided insight into ancient numbers, the Sumerians had already developed a complex arithmetic.

[29][30][31] A decimal version of the sexagesimal number system, today called Assyro-Babylonian Common, developed in the second millennium BCE, reflecting the increased influence of Semitic peoples like the Akkadians and Eblaites; while today it is less well known than its sexagesimal counterpart, it would eventually become the dominant system used throughout the region, especially as Sumerian cultural influence began to wane.