in maths history

The history of counting

The past is full of mathematical geniuses; Da Vinci, Newton, Einstein, and Carl Friedrich Gauss. When he was 7 years old he was asked by his school teacher to add together all of the numbers from 1 to 100. It took him just seconds to give the right answer. Here’s what he realised: 1+100=101, 2+99=101, 3+98=101, which is 50 pairs. So the sum of all the numbers is 50 times 101. 50 times 100 is 5000, plus 1 times 50, which 5050. His teacher was astounded. The teacher didn’t know it at the time, but Gauss went on to become a maths genius.

Modern maths has more than 50 different fields or topics, like algebra, geometry, trigonometry, statistics, etc. And some topics, like calculus, is so complicated it can be studied up to your final years at University. Maths is a diverse and varied subject that has a rich and fascinating history, and it all starts with counting.

Maths goes back a long way. The Babylonians, Egyptians, Greeks, the Islamic civilisation and even the renaissance all created many great maths scholars. But it’s a deceptively simple subject that started life many thousands of years ago in very practical ways, based on simple counting systems.

Palaeolithic man made stone axes in perfect proportion, so that the ratio of the width to the length of the axe was always the same. This made the axe an effective weapon. They discovered this through trial and error. Perhaps they discovered the golden ratio before the Greeks did. The golden ratio is commonly found in nature and used to create visually pleasing designs by modern-day artists and designers.

It’s well known that our counting system today uses base 10 or decimal, which is counting in factors of 10. And it’s thought that the reason for this is we have 10 fingers on our hands. Simple and logical. If you’ve heard of tally sticks, one of the first was made from animal bones with notches to record numbers. Tally sticks were used throughout history to store important numbers. They were even used in Medieval England to record tax income by the Exchequer. Eventually they were superceeded by better counting methods, but not until a few hundred years ago.

The Incas used knotted string for counting and to record tax revenue. And it has been suggested that the Ishango bone is a lunar calendar, although it’s not proven. Counting numbers and recording them permanently has a long history.

Although we count to base 10, earlier civilisations used a different base. The Gumulgal system counted to base 2, which interestingly enough, is how computers count. They use binary. And the Kamilaroi system counted to base 3. Recent research in the US revealed that most of the North American tribespeople counted to base 10. The widespread use of base 10 in the long history of counting is probably why we use it today. What’s even more interesting is early cultures created lunar calendars and star maps too, a useful application of counting.

What we can deduce from this is that counting numbers has a very long history, going back hundreds of thousands of years, and is the foundation of modern maths.

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