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The Invention of Mathematics

Updated on January 12, 2014

Maths is everywhere. It's learnt in school, and we count things every day. However, numbers are a man-made creation (along with things like time).

People learned to count thousands of years ago. I mean, our ancestors lived fine without numbers for a few millions of years, where they lived in caves and hunted wild animals. However, when they finally started settling down into colonies and building bigger accommodations, the invention of numbers was something that had to occur.

Think about it. They’d need numbers to count how many crops they had, how many sheep they needed to sell at the market... Because the first farms and the first towns appeared in the Middle East, so did the first numbers.

Recording Numbers

People started counting on fingers first, which worked quite well (and it still does!). But fingers are quite a basic number counting system, and do not help you to remember a lot of stuff. So humans began to make the first number records by dropping stones, shells of clay and disks one by one into a bag.

6,000 years ago in Sumeria, someone developed the great idea of making scratch marks onto a clay tablet – one mark for each thing they were counting. This was very much like the glorious tally charts we use today! But you know how crowded tally charts can get once there is too much information to record.

Soon, the Babylonians learned to use different shaped marks for larger numbers. Their system is the basis of our modern number system – but instead of using different marks for larger numbers, we simply use a different symbol for each number up to nine and then put the symbols in different positions for the larger numbers.

An ancient abacus.
An ancient abacus.


Early civilizations also developed mathematical skills. First, there was arithmetic – the art of working out things using numbers by addition, subtraction, multiplication and division. Arithmetic is extremely old – the oldest of all the mathematical skills.

Due to records, we know that the Babylonians and Sumerians were skilled in arithmetic at least 5,000 years ago. Babylonian school kids learned how to multiply and divide using arithmetical tables to help with complex sums.

Arithmetic was developed to keep the accounts that were the key to power in the ancient civilizations. This was vital – for example, it helped to work out how much tax people owed. To keep track of tax accounts and payments, they scratched marks on soft clay tables which hardened to make a permanent record.

Skills in arithmetic were highly honored, and often even feared. Thousands of years ago, people were firm believers in magic. Quick mathematic calculations that solved complicated problems seemed like magic – this was the first time people had ever witnessed something like that.

The arithmetic processes developed in ancient China appeared to be so tricky and clever that they were still being used by Chinese “mind-readers” in the music halls of Europe in the early 20th century.


Another valued skill was geometry – the mathematics of shapes. The first great masters of geometry were the ancient Greeks, such as Pythagoras, Eudoxus and Euclid, who lived between about 330 and 275 BC. Geometry is a Greek word meaning “earth measurement”. Euclid’s book Elements is a brilliant study of geometry. Even today, mathematicians still refer to all the geometry of flat surfaces (lines, points, shapes and solids) as Euclidean geometry.

It was probably first invented to help people work out the area of their land. Geometry was developed by the ancient Egyptians over 4,000 years ago to help them build perfect pyramids.

The Great Pyramids still amaze and astonish us with their geometric precision. Many think that aliens built them, not the ancient Egyptians. After all, these are thousands of years old structures that are still standing – modern buildings usually can’t last for over one hundred years.

However, an amazing discovery showed us how they did it. The Scottish historian Alexander Rhind was out holidaying in Egypt in 1858, when he bought an ancient papyrus written by an Egyptian scribe named Ahmes from around 1650 BC. This papyrus showed that the ancient Egyptians knew a great deal about the geometry of triangles. For example, they knew how to work out the height of a pyramid from the length of its shadow on the ground. Now that’s clever.

Which area of mathematics do you enjoy the most?

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Great summary video on the history of mathematics:


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