A Brief History

How did mathematics begin?

Human beings from our earliest beginnings have searched for solutions to basic problems such as building homes, measuring space, keeping track of seasons and counting objects.

An artist's rendition of the early cavemen. Image credit: http://fubini.swarthmore.edu

Over 30,000 years ago, early Paleolithic people kept track of the passing seasons and the changes of weather for planting. To represent the passing of time, they carved tally marks \((\require{cancel}\cancel{||||} \; ||)\) on cave walls or slash \((/)\) tallies on bones, wood or stone. See the image below.

Tally marks on cave wall. Image credit: public domain

Each tally stood for one. However, this system was awkward when it came to large amounts, so symbols were eventually created that stood for groups of objects. In fact, sumerian clay stones have been found to date back to fourth millennium BC. A small clay stone was used for 1, a clay ball was used for ten and a large cone stood for 60.

Image credit: Pinterest

Written records from around 3300 BC show that Babylonians inscribed amounts on clay tablets with a reed (see image above). They used a nail shape for ones and a "V" on its side for tens \((<)\), combining these symbols to write other numbers. For example, see the way the Babylonians wrote the number 12 in the image above.

The ancient Egyptians used objects from everyday life as symbols. A rod stood for one. A cattle hobble was ten. A coiled rope was 100. A lotus flower was a thousand and so on. The number 12 was a cattle hobble and two rods. See the figure below for an illustration.

Image credit: Slideshare

The early Romans created a number system (see figure below) that we still see today. Along with other symbols, they used an \(\text{X}\) for \(10\) and an \(\text{I}\) for \(1\). By the Middle Ages, Romans were putting the \(\text{I}\) to the right of the \(\text{X}\) for \(11\) and to the left for \(9\), so they wrote \(19\) as \(\text{XIX}\).

Image credit: Pinterest

All these creative number systems show groups of objects as well as individual objects. Some of the oldest human counting systems rely on fingers and toes, so they were based on ones, fives, tens and twenties. The Zulu words for six means "to take the thumb of the right hand" meaning that all the fingers on the left hand had been added up and the other thumb was needed.

Other systems evolved from commerce. The Yoruba in Nigeria used calorie shells (see image below) as currency and developed an amazingly complex number system which was based on twenties and on the operations of multiplication, subtraction and addition. For example, they thought of 45 as three times twenty minus ten minus five.

Image credit: Wikimedia Commons

Knots tied in cords and strings were used for recording amounts by many cultures like the Persians. The Incas used a more refined version called a "quipu" or "khipu", a thick cord held horizontally from which hung a knotted string. The kind of knot the Incas used along with the length and colour of the cord represented ones, tens and hundreds. See the image below.