History of ancient numeral systems

The first method of counting was counting on fingers. This evolved into sign language for the hand-to-eye communication of numbers which, while not writing, gave way to written numbers.

Tallies made by carving notches in wood, bone, and stone were used for at least forty thousand years. Stone age cultures, including ancient Native American groups, used tallies for gambling with horses, slaves, personal services and trade goods.

Roman numerals evolved from this primitive system of cutting notches. It was once believed that they came from alphabetic symbols or from pictographs, but these theories have been disproved.

The earliest known writing for record keeping evolved from a system of counting using small clay tokens. The earliest tokens now known are those from two sites in the Zagros region of Iran: Tepe Asiab and Ganj-i-Dareh Tepe.

To create a record that represented "two sheep", they selected two round clay tokens each having a + sign baked into it. Each token represented one sheep. Representing a hundred sheep with a hundred tokens would be impractical, so they invented different clay tokens to represent different numbers of each specific commodity, and by 4000 BC strung the tokens like beads on a string. There was a token for one sheep, a different token for ten sheep, a different token for ten goats, etc. Thirty-two sheep would be represented by three ten-sheep tokens followed on the string by two one-sheep tokens.

To ensure that nobody could alter the number and type of tokens, they invented a clay envelope shaped like a hollow ball into which the tokens on a string were placed, sealed, and baked. If anybody disputed the number, they could break open the clay envelope and do a recount. To avoid unnecessary damage to the record, they pressed archaic number signs and witness seals on the outside of the envelope before it was baked, each sign similar in shape to the tokens they represented. Since there was seldom any need to break open the envelope, the signs on the outside became the first written language for writing numbers in clay. An alternative method was to seal the knot in each string of tokens with a solid oblong bulla of clay having impressed symbols, while the string of tokens dangled outside of the bulla.

Beginning about 3500 BC the tokens and envelopes were replaced by numerals impressed with a round stylus at different angles in flat clay tablets which were then baked. A sharp stylus was used to carve pictographs representing various tokens. Each sign represented both the commodity being counted and the quantity or volume of that commodity.

Abstract numerals, dissociated from the thing being counted, were invented about 3100 BC. The things being counted were indicated by pictographs carved with a sharp stylus next to round-stylus numerals.

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