# Where do our numerals come from? A short history of the Indo-Arabic numeral system

Did you know that until the 15th century AD the majority of people in medieval England were still using Roman numerals to write out dates and numbers? We take for granted being able to use the numbers 1-9 to do arithmetic, write out dates, calculate our taxes, and generally help us navigate the modern world we live in today. However, this clever system is a relatively new phenomenon to Europe, which gradually replaced the cumbersome Roman numeral system (I, II, III, IV…) which was in use until well into late medieval Europe.

So where did our “new” numeral system (0, 1, 2, 3…) come from? And why do we call them ‘Indo-Arabic numerals’ if they are different to the numerals currently in use in the Middle East (٠,١,٢,٣…) and in India (०, १, २, ३…)?

In this blog post we will look at the history and development of the Indo-Arabic numeral systems, and see how they spread westwards from the Middle East, and compare the different numeral systems now in use across many parts of the world today.

### Background

The earliest counting systems in the world are thought to be quinary (base 5), which developed from simply counting the fingers on your hand. Other early counting systems were decimal (base 10: counting with both hands), and vegesimal (base 20: counting with the hands and the toes). We have a record of early numeral systems from Egypt (5400 years ago), China (3600 years ago), and Elam in Mesopotamia (over 3000 years ago). The Sumerians and Babylonians in Ancient Mesopotamia used a sexagesimal system (base 60). Nowadays, the decimal system is by far the most common counting system used around the world, thanks in part to the spread of the Indo-Arabic numerals.

Before there were specific symbols for each number, the easiest way of counting was using your fingers, called dactylonomy, انگشت‌شماری angosht-shomāri or حساب العُقود hesāb ol-’oqud in Arabic. Later on, the Arabs began to use letters of the alphabet to represent a specific number, for example the letter ب B represented the number 2. This system is called حروف ابجد horuf-e abjadabjad numerals’.

### History of the Indo-Arabic numerals

The predecessor to our current system is the Brahmi numeral system, which was used in India since at least the 4th century BC. By the 8th century AD, the Indian numerals were slowly starting to spread westwards…

In 825 AD, the famous Persian mathematician and philosopher خوارزمی Khārazmi (or Khwārizmi) wrote a book which introduced Greater Persia and the Middle East region to the اعداد هندی a’dād-e hendi ‘Indian numbers’. This book, called the حساب هند hesāb-e hend, is ultimately responsible for spreading this numeral system across Persia and the Middle East, where its benefits were quickly realised by the 9th century Islamic scholars.

### ‘0’ Zero صفر Sefr : the key to the whole system

The ingenuity of the Indo-Arabic numeral system lies in its use of positional notation, also called place-value notation. In simple terms, positional notation refers to a system where each digit in a sequence gets multiplied by its place value. This sounds complicated at first and it’s a hard idea to wrap your head around, because this concept is so ingrained in us from an early age, it feels like we use positional notation sort of instinctively. To understand it better, let’s look at an example of positional notation in action:

Here we can see that the place value of ‘hundreds’ is ten times the place value of ‘tens’, and so on. Positional notation works in contrast to a system like the Roman numerals, where a numeral like X (10) will always represent 10 regardless of its place value in a sequence.

The key to positional notion is the symbol 0 ‘zero’, used to indicate the absence of a number in a place. For example, in the number 102, the ‘0’ indicates that there is no digit in the ‘tens’ column.

The ancient Babylonian mathmatians (around 2000 BC) were the first to use a zero-like symbol to signify an empty positional value. It appears that the Babylonians were also the first to start using a positional notation system. The Maya people of Central America also independently developed a zero-like placeholder symbol, as did the Chinese.

However, our modern ‘0’ zero symbol is thought to have developed from the Indians, who used a large dot to represent both ‘nothing, null, void’ as well as ‘an empty positional value in decimal place-value notation’. The Sanskrit word for this symbol is śūnya, and dates back to as far as ~300 BC. Khārazmi comments on the Indian usage of 0 ‘zero’ to mark an empty place-value notation in his book حسابِ هند hesāb-e hend

### Transmission to Europe

“Numerals will follow trade, and the interchange of goods reaches further than the march of armies or the spread of religion, law or learning.” – Wright (page 105)

As the usage of these Indo-Arabic numerals began to spread across the Middle East in the 9th and 10th centuries, the forms of the various symbols began to diverge. In the most western of the Islamic countries (North Africa and Andalusia) a western variant began to develop, which became known as the غُبار ghobār ‘dust’ numerals. The numbers which we use in Europe today (0, 1, 2, 3…) developed from these dust numerals, brought to Northern Europe thanks to the Moors of Iberia. That is why in English today, we still call these numerals ‘Arabic numerals’, ‘Indo-Arabic numerals’, or more correctly, ‘Western Arabic numerals’. However these numerals took an awfully long time to catch on in Europe.

Towards the end of the 12th century, the Italian mathematician Leonardo Bonacci, more commonly known by his moniker ‘Fibonacci’, became acquainted with the Western غُبار ghobār ‘dust’ numerals while he was a young boy. Fibonacci’s father worked in Algeria, so from an early age he saw these numerals being used by people living on the North African coast. The more Fibonacci travelled around the Mediterranean, the more he began to realise the advantages of the Indo-Arabic numeral system, instead of the rather tedious Roman numeral system.

In 1202 AD, Fibonacci wrote a book called Liber Abaci ‘the Book of the Abacus’, where he introduces modus Indorum ‘the method of the Indians’ to European scholars. This new way of counting slowly began to spread through Europe between the 13th and 15th centuries. During this time, Europeans started using both systems simultaneously, for example, scientists and mathematicians began to use the Indo-Arabic system for their calculations, but merchants and bookkeepers were more hesitant to make the change and continued to use Roman numerals. When the English poet Chaucer encountered the new numbers, he called them ‘noumbres of augrim’ [‘numbers of algorithm’]. A 14th century book of English mathematics also refers to them as ‘fyguris of Inde’ [‘figures of India’].

Gradually, the convenience of the Indo-Arabic numerals was slowly realised by the Europeans, and by the end of the 15th century they had become commonplace in medieval England.

### Eastern vs Western

As we have already explored, the numerals which entered into Europe were the Western variation, originating from the مَغرِب Maghreb ‘Northwest Africa’: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These Western numerals are used today all over the world, including in Europe, the Americas, Morocco, Algeria, Tunisia, and Libya.

To the East of the Maghreb, a different variation of these numbers is used, called the ‘Eastern Arabic numerals’. These are the numerals that hopefully as a Persian learner you will already be familiar with: ۰, ۱, ۲, ۳, ۴, ۵, ۶, ۷, ۸, ۹.

These numerals are used in Iran, Afghanistan, Pakistan, and the مشرق Mashreq ‘the Eastern part of the Middle East’. In Egypt, Sudan, the countries around the Persian Gulf, and countries of the Levant, both Eastern and Western systems are currently in use. This is because there is a recent trend across the world to use Western Arabic numerals more and more, this can even be seen happening in China and Japan.

However, to make matters more confusing, the Eastern Arabic numerals for 4, 5, and 6 have slight variations depending on the region. Below is a table summarising the differences:

 The Western Arab World 0 1 2 3 4 5 6 7 8 9 Persian* (Iran and Afghanistan) ٠ ١ ٢ ٣ ۴ ۵ ۶ ٧ ٨ ٩ The Eastern Arab World ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩

*as well as other languages which use the Perso-Arabic script, such as Urdu and Kashmiri.

As always, we hope this blog was informative, and gave you a little glimpse into a fascinating history tale which took us all the way from Ancient Mesopotamia to the times of Fibonacci and Chaucer in medieval Europe!

– Sam

### Select References

Bishtawi, A. S. (2011). Origin of the Arabic Numerals: a Natural History of Numbers. Bloomington: AuthorHouse.

Wright, G. G. N. (1952). The Writing of Arabic Numerals. London: University of London Press Ltd.