Sumerian & Babylonian Number System: Base 60 A rudimentary model of the abacus was probably in use in Sumeria from as early as 2700 – 2300 BCE. Over the course of the third millennium, these objects were replaced by cuneiform equivalents so that numbers could be written with the same stylus that was being used for the words in the text. Starting as early as the 4th millennium BCE, they began using a small clay cone to represent one, a clay ball for ten, and a large cone for sixty. They moved from using separate tokens or symbols to represent sheaves of wheat, jars of oil, etc, to the more abstract use of a symbol for specific numbers of anything. They were perhaps the first people to assign symbols to groups of objects in an attempt to make the description of larger numbers easier. In addition, the Sumerians and Babylonians needed to describe quite large numbers as they attempted to chart the course of the night sky and develop their sophisticated lunar calendar. Indeed, we even have what appear to school exercises in arithmetic and geometric problems.Īs in Egypt, Sumerian mathematics initially developed largely as a response to bureaucratic needs when their civilization settled and developed agriculture (possibly as early as the 6th millennium BCE) for the measurement of plots of land, the taxation of individuals, etc. The Sumerians developed the earliest known writing system – a pictographic writing system known as cuneiform script, using wedge-shaped characters inscribed on baked clay tablets – and this has meant that we actually have more knowledge of ancient Sumerian and Babylonian mathematics than of early Egyptian mathematics. The Babylonians used only two symbols to represent their numbers: the "wedge" marked tens and the "nail" marked ones.Sumer (a region of Mesopotamia, modern-day Iraq) was the birthplace of writing, the wheel, agriculture, the arch, the plow, irrigation and many other innovations, and is often referred to as the Cradle of Civilization. ( TAMU Web Article - Babylonian Mathematics) An example would be rewriting the mixed number 3 24/60 as 3 14 in Babylonian notation. The symbol of the semicolon is known as a 'seperatrix' notation. The way they would write this was in the form a b, where a is the whole part, and b is the fractional part, which had to be a number less than 60 (since that was their base). (The Story of Numbers, 32) Besides their development in whole number notations, they also used notations for fractional parts too. Their knowledge of mathematics skyrocketed, once they had taken over the Sumerian empire in the early 20th century B.C. This new development greatly increased their effectiveness in growing the field of Mathematics. Meanwhile, 60^4 is 12,960,000 which contains 225 divisors! This large number of divisors in turn makes addition, subtraction, multiplication, and division much easier to work with! ( The Magic of Numbers, pages 24&26)īabylonian mathematics introduced a place-value system including a primitive form of "0" which was used to describe that there was no value of a particular order. Ten to the power of four is 10,000 which only contains 25 divisors. This difference only gets bigger when we consider these two bases taken to their fourth power. Ten has only four divisors, whereas 60 has 12 divisors.
This system was chosen most likely out of its friendliness to factoring. This number system is based on the number 60, rather than the usual decimal counting of tens.
The Babylonians used a very different number system from what is normally seen today.