The Discovery of Numerals and Dash

Based on the book Liber Abacci by great Italian mathematician, Leonardo Pisano, otherwise known as Fibonacci. What’s fascinating is that on page 406 is a reference to an older text called modum algebre et almuchabale and in the margin is the name Maumeht, which is the Latinised version of the Arabic name, Mohammed. The person he’s referring to is Mohammed ibn Musa Al-Khwarizmi.

In fact, Arabic names crop up in many medieval European texts on subjects as varied as map-making, optics and medicine. But I want to start with Al-Khawarizmi, because his work touches on a crucial aspect of all our lives today. It’s thanks to Al-Khwarizmi that the European world realized that their way of doing arithmetic, which was still essentially based on Roman numerals was hopelessly inefficient and downright clunky.

If I asked you to multiply 123 by 11, you may even be able to do it in your head. The answer is 1,353. But try doing it with Roman numerals, you’d have to multiply

CXXIII x XI = (C x X + C x I) + (X x X + X x I) + (X x X + X x I) + (I x X + I x I) + (I x X + I x I) + (I x X + I x I)
= (M + C) + (C + X) + (C + X) + (X + I) + (X + I) + (X + I)

It can be done, but trust me, it’s not fun. Al Khwarizmi showed Europeans that there’s a better way of doing arithmetic. In his book entitled The Hindu Art of Reckoning, he describes a revolutionary idea. You can represent any number you like with just ten simple symbols.

Indian Arabic numeralsThe idea of using just ten symbols, the digits from one to nine, plus a  symbol for zero to represent all number from one to infinity was first developed by Indian mathematicians around the 6th century and I can’t overstate its importance. Let me show you. Here are the numbers in Indian Arabic numerals. Wahid, ithinin, thalatha, arba’a, khamsa, sita, saba’a thamania, tisa’a. And here are the numbers we’re more familiar with in the West. One, two, three, four, five, six, seven, eight, nine. And you can see the similarity between these numbers and particularly between the numbers two and three, if I tip this sideways, you can see how they look like numbers two and three.

And what’s powerful about this digits, this numerical system is how it simplifies arithmetic calculations. But Al-Khwarizmi and his colleagues went further than just translating the Indian system into Arabic. ‘They created the decimal point’.

Dash This text, written just a century after Al-Khwarizmi’s is by a man we know as only as Al-Uqlidisi. Here, he shows that the same decimal systems can be extended to describe not just whole numbers but fractions as well. The infinity of possibilities that lie in between the integers.  Here is a copy of Al-Uqlidisi’s manuscript where he showed how the decimal point is used for the very first time. He describes it by using a dash. Here are the digits 17968, and there’s a small dash over the nine indicating the decimal place.

The idea of the decimal point is so familiar to us, that it’s hard to understand how people managed without it. Like all great science, it’s blindingly obvious after it’s been discovered

Jim Al-Khalili, Professor of Physics at The University of Surrey
BBC Science and Islam

I suppose C=100, X=10, I=1, M=1000, L=5 in Roman numerals, am I right? I just pretending hehe. It’s so prodigious don’t you think? How the finding of numerals 1-9 and 0 and a dash to define decimals and fractions are one of the bigest discovery ever had. Asking about why it should be like this or where it is came from are much interesting to find out than solve the question its self, that’s what I think. What an epic side of science 🙂


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