Math of the Moors
In 711 AD, barely 100 years after the establishment of Islam, the Moors crossed over from Northern Africa and conquered most of Spain. Many of the anti-Catholic Christians and Jews resident in Spain did not see the invasion as a totally Bad Thing, since the Moors showed religious tolerance - more than the Catholics did - and made many improvements.
The Moors brought with them a richness of culture and learning that was sorely missing from Medieval Christian society. Arriving with translations of the Greek masters (Archimedes, Pythagoras and the philosopher Ptolemy), the Moors established robust institutions of learning, including well-stocked libraries. They set about improving agriculture, astronomy, architecture, science and mathematics. They called their new land Al-Andalus.
The locals were still using the Roman numeral system (I, II, III, IV, …), but the Moors introduced a much better system of numbers (derived from India via the middle east and Alexandria), called the Hindu-Arabic number system.
Hindu Arabic numbers
The big deal about the new number system was that it was positional. This means that for a large number containing several digits, the further to the left you go, the larger the value of the digit. Each position to the left represents a multiple of 10.
For example, four thousand, three hundred and sixty five in the new system was written 4,365 and the value of the digits means:
1000 | 100 | 10 | 1 4 | 3 | 6 | 5
The same number in Roman numerals was written MMMMCCCLXV (4 × 1000 + 3 × 100 + 50 + 10 + 5). It was quite difficult to perform calculations with such a cumbersome system.
Here’s what Hindu-Arabic numerals looked like by about 1000 AD. We can see that they resemble closely the numbers we use today.
A Violent End
The Moors were advanced technically and had established a very enlightened society for the time. Unfortunately, they were too complacent about their enemies and they let their guard down. Eventually the Catholics attacked from the north and took over the whole of Spain by 1492. This was after they terrorised the Moors for hundreds of years by requiring conversion to Catholicism or face expulsion. The ones who were found to be not “Catholic enough” were sent off for torture in the Inquisition. Eventually, the remaining few hundred thousand were ethnically cleansed and sent packing to North Africa or beyond. It was a tragic end to an inspiring flowering of learning and discovery.
In fact, the Moors had a large influence on the beginning of the Renaissance (around 1450) in other parts of Europe. The universities of Paris and Oxford were established as a result of visits by scholars to Al-Andalus.
Contributions of the Moors
We get many mathematical concepts (and words) from (or via) the Moors, including:
- algebra
- algorithm
- zero (from “zephirum”)
The article Leonard of Pisa (Fibonacci) and Arabic Arithmetic is a very interesting outline of how Fibonacci regarded Muslim mathematics.
End Bit
It is a tragedy that these people who contributed so much were snuffed out. The Spanish have chosen to ignore many of the details of this episode from their history. The winners will always get to interpret history how they like.
The Moors deserve more credit.
Update: The invention of the antennae in this Fractal Tiling Arrays article was inspired by the intricate tiling of the Alhambra mosque.
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Thomas Jones said,
March 24, 2008 at 7:18 am
In regards to your website,I accept the idea of the Moor,s and the Spanish. But what about the Portuguese involvement in and on the Iberian peninsula,as well as their fight with the Spanish for their independence.
zac said,
March 24, 2008 at 2:24 pm
Hi Thomas and thanks for your clarification. Yes, the Portuguese were also instrumental in the rout of the Moors from the Iberian region.
And the Portuguese also benefited from the scholarship of the Moors, becoming a great seafaring nation a few hundred years later.
Aldebaran said,
April 4, 2008 at 9:33 am
It is clear you are not pro-Catholic. That you have a bias in favor of Moorish invaders, possibly coming from a singular, narrow-minded and blinded perspective of seeing those who “disseminate” mathematics as a major basis to judge whether people are good/better or not. You are definitely NOT a Spaniard. Do not cast aspersions on others of a period of time who sought freedom from invaders. Who struggled for hundreds of years to regain the lands that were taken from them by invaders. Consider Gandhi and his movement against British imperialism. It is because people FAIL to see as well as FORGET the overwhelming need that human beings have for freedom, that these lessons have to be relearned over and over again. The Spaniards conquest of the indigenous peoples of the Americas. They brought all kinds of technological and even mathematical improvements to those they dominated. No doubt in this debate you would take the side of the native Americans and not the Spaniards. Hypocrisy! Open your eyes!
“The victims of the past become the oppressors of the future.”
zac said,
April 4, 2008 at 10:37 am
Thanks for your comment Aldebaran.
I am certainly not in favour of invaders of any colour or creed. You have misconstrued what I wrote and added things that are not there.
My bias is towards freedom and education - and one aspect of that freedom is proper recognition and promotion of educational achievement. My interests are far broader than the dissemination of mathematics.
Don’t assume what my “side” would be in any historical situation.
Richard Coeur de Lion said,
May 7, 2008 at 10:31 pm
I find your comments on the Maths of the Moors fair and appropriate.
It’s a shame that some narrow-minded bigots blinded by hatred won’t digest the historical facts. The irony is that one person fumes and rages and pretends to defend freedom-fighters whilst two sentences later he praises the Spaniards for having brought tech and math to the native Americans, conveniently turning a blind eye to the massacre of the natives and the plundering of their gold. And look who dares to accuse others of hypocrisy!
Jesus was right in blasting the Pharisees and those who look for the straw in the eye of their neighbour but forget the log in their own!!
By the way, Aldebaran is Arabic for “The Follower”. Follower? Of Jesus or of the Spanish Inquisition??
It is clear that bigots and racists cannot truly claim to follow Jesus.
zac said,
May 7, 2008 at 10:43 pm
Thanks, Richard. I was also rather taken aback by Aldebaran’s insinuation that the Spanish invasion of the Americas was a ‘good thing’, but it was not very clear what (s)he was getting at there.
I’m sure the original inhabitants of the Americas felt they could do without the European’s math and science at the time.