Math of the Moors

By Murray Bourne, 07 Feb 2007

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.

Alhambra
The Alhambra

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.

Hindu Arabic numerals


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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27 Comments on “Math of the Moors”

  1. Thomas Jones says:

    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.

  2. Murray says:

    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.

  3. Aldebaran says:

    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.”

  4. Murray says:

    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.

  5. Richard Coeur de Lion says:

    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.

  6. Murray says:

    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.

  7. mariam says:

    Hi,i just wanted to say that “the moors” that you are talking about are actually muslims whether you believe it or not(if you donot,then by looking at the history of spain,you’ll realize that it was ruled by muslims for about 800 years),so “the moors” are muslims!

    and,i am not being bias…..i am just being factual!

    please,correct the word “moor” used for muslims….

  8. Murray says:

    Hi Mariam. My first sentence says “barely 100 years after the establishment of Islam” where I meant the Moors were Muslims.

    But it was not clear enough obviously. Thanks for the clarification.

  9. Candice says:

    The Moors were and are not the Muslims of today that we think of today or then. The Moors had a rather RICH history i.e. Benjamin Bannaka (Banneker) was a Moor. There were/are many so called “Native American” indigenous tribes that were of Moorish heritage i.e. Washitaw, Cherokee, Yamasee, Seminole etc. The U.S. before it was the “U.S.”, was owned by Moors (indigenous tribes) and acres have been sold illegally violating many treaties that the U.S. signed with the Moors. The Washitaw Moors were granted over 60K acres of land in Louisiana in the 1990’s due to the violation of the Treaty of Friendship and Peace signed between Morroco and the U.S. This historical memory that was stripped from so called “Black Native Americans” and this was the objective of slavery and why if blacks were caught reading they were tortured. Sorry for the long story…but it is just enough to get those interested into researching the the true history of us all. These are facts and not intended to be racially biased in any way, shape, form or fashion. Peace & Blessings. Hotep.

  10. Fred says:

    Dear readers,
    My friend Candice has probably never looked at a history book before. The Moors, never had anything to do with the Americans. The never even co-existed. All that nonsense that she’s babling about is 100% fiction. Don’t believe me, just and check it out for yourself. I can tell you a fact, the Moors were long dead before the 20th century.

  11. leon says:

    The last comment pertaining to the end of the moors before the twentieth century. You are misinfomed. You need to do some research about the Moors. Better still research poverty point located in louisiana. You will find we are alive and well, and have emperical proof of our existence over a 100,000 years. thats right, right here in North America. Dont argue do the research. Washitaw Dedugdahmoundyah.

  12. Fred says:

    Leon, one can connect himself with any nation as long as one has the genetic proof. According to wikipedia, the Treaty of Friendship and Peace between Morroco and the U.S. , was signed in 1786. If you know the history of the Moors in the liberian penisula, the Moors were expelled in the Reconquista, which ended on January 2, 1492 with the conquest of Granada. The original Moors had been wiped out. If I was Turkish, I couldn’t connect myself to the great Ottoman empire, it lasted to the 1920’s but its glory was deministed. It was because they had given up their culture and heritage, just like the Moors. So you see you might be Moorish but you are not connected in any way to the great empire of the Moors because you do not practise their religion, and culture. If you have any other comments please do reply.

  13. Z says:

    Prince Charles gave a lecture at oxford university on the 27th of october 1993 and he reminded the wise scholars of the debt that the west owed to the Moors. They also introduced and expanded on astronomy, law, history, pharmacology, architecture to name a few. Prince Charles stated that in the tenth century moors had lending Libraries when the English King, Alfred was still eating human flesh.

  14. Win says:

    In this Moors teaching Spain ( and Europe ) some culture, maths, astronomy, pharmacology etc., it seems that Moors ( or Muslims or Arabs ) themselves learnt all such subjects from India. All great Muslim scholars were aware of Supreme richness of India ( in terms of depth of all above subjects and money wise, both ) and they have themselves translated those vast books into Arabic from Sanskrit.

    Though early Moors were pro towards knowledge and Muslim invaders in India razed down university towns like Taxila and Nalanda. Indians very highly advanced even at 3000 BC period when they had constructed large planned towns. And that time English people were definitely eating human flash and were savage ! Spain king helped Columbous on his mission to find sea route to India ( and America wasn’t known then ). It was such a lull of Indian richness. If Moors had not transmitted Indian Maths, seafaring & astronomy would have been impossible and Spain / Portugal would not have dared to plunge into deep ocean waters to find Indian sea route.

    I feel pity of English people who misguided the world for two centuries about India to show themselves as culturally superior to Indians !

  15. Leon says:

    Hotep to all my Muur Brothers and Sisters. Fred do you know who the original man is? Fred do you know what Asiatic, Mu, and the Earth have in common ? Fred have you checked into Poverty Point located in Louisiana and researched anything about the Mound Builders. Fred do you know anything about the Mounds that are still in existence throughout the Americas. Americas is not a typo its meant to entail all the Americas. If the History hadnt been destroyed by Marco Polo, and Alexander The Greek by burning and destroying books the history of the world wouldnt be in such a Historic quandary today. Also the Hieroglyphics in The Grand Canyon area along with the discovery of an 9,000 year old Mummy dont lie about our existence here in the Americas. Washitaw Dedugdahmoundyah. Fred in case your wondering NO I AM NOT BLACK.

  16. Leon says:

    Fred I was just a little curious as to what the Moors religion is according to your source. Amexem is the name of the Muur Empire

    Hotep,
    My Texas

  17. Shaluh Kufu EL says:

    Hotep/Salaam/Shalum. I came across this sight by accident and found it very interesting. It mind boggles me on how superficial people are when it comes to History. It is just that His Story, someone else’s interpretation of past events. The Moors were definately inhabiting the Americas( Amir-Ri/Re-Ka) before any European even set foot on this soil. The Native Americans(American Indians) that we know of are a mixture of the Moorish/African nations of people that migrated here to America. The word “Indi” means black and when Christopher Columbus arrived in the Carribean and the Americas he said the indigenious people were “Indi’s” or Indians, meaning Black peoples. We come in many shades of Brown regardless of the ethnic make up. Moorish/Nubian/African empires were all over the planet. The evidence does not lie, you can find ancient Moorish/African artifacts throughout the Americas from Louisiana, Georgia, Carolinas, Mississippi, Tennessee, Ohio, Canada, California, etc. The state of California was named after a Moorish/African women name Queen Califia/Khalifia. This is a fact and can be researched. Also when I say Moor or Moorish I am not just talking about certain Moors that occupied Europe. The term Moor/Mauri/Moriscos/Morenos/Maure all stem back to Khemet or Ancient Tamare. Can you see it TA MA RE . TA= Earth MA= Water, RE= Sun. So MARE’s or MARE NU would translate as Water&Sun People which the Ancient Kushites, Nubians, Khemites were known as. These are also 3 of the five elements coming from Khemetic/Moorish Sciences. The Moors are still alive and well, we did not go anywhere we are just known under different names nowadays. The Sciences are still alive, everytime you do Geometry, Algerbra, Calculus, tell time, check your calendar you are bearing witness to sciences of the Moors/Mare’s.

  18. The Facts says:

    Shaluh Kufu EL said, “The state of California was named after a Moorish/African women name Queen Califia/Khalifia. This is a fact and can be researched.”

    I did some research and found that “Califia (aka Calafia) is the name of a legendary Black Amazon warrior queen, associated with the mythical Island of California. The US state of California is thought by some to be named after Queen Califia (see Origin of the name California).”

    http://en.wikipedia.org/wiki/Queen_Califia

    http://en.wikipedia.org/wiki/Origin_of_the_name_California

    It seems some people like to leave out key pieces of information in order to make what they say more believable.

  19. Murray says:

    Thanks for the input, however I would suggest not using Wikipedia for such “proving” of facts. Those articles may be written (or edited) by people with an agenda.

  20. Shaluh Kufu EL says:

    Peace. The facts said “It seems some people like to leave out key pieces of information in order to make what they say more believable.” You are absolutely right, You have some researchers that have and still do leave key pieces of information out especially if it doesnot comply with conventional information.
    If certain information does not matchup with the popular mindset it will be shelved or in some extreme situations destroyed. This has been going on for a long period of time, it is a known fact that the history books need to be rewritten due to the many facts that have proven a lot of things to be outdated.

  21. malbit says:

    wow. ppl in this site are intense.

  22. Eliza says:

    Zac Is correct! You cannot rely on Wikipedia for accurate information. Anyone can, at any time,change what is written there and input their own words. When I heard of this I tried it and it worked. I reversed what I had fiddled with but not everyone does. There is a lot of debateable information out there from books written in the beginnings up to present time and everyone wants to be correct…this is how wars begin! Consider your source, be guided by wisdom and appreciate the voices of others even if you don’t happen to agree.

  23. Alessandro says:

    I think a mathematician should remain a mathematician. Such a biased view of the Spain “reconquista” is only harming this website. The Muslim occupation of Spain all Southern Mediterranean countries was through war and an apartheid-like social system. It’s much debated whether the muslims, “Moors” (the word comes from “black”,darker skin, being many African, obviously; “mori” means dark, black in Italian) and “arabs” (actually mainly Iranians, not arabs) did really contributed significantly more than taking Indian and Greek knowledge and traditions and passing it on. That the Moors had great influence in the Renaissance is a total non-sense. Renaissance occurred mainly in Italy where music, architecture, banks and finance, arts, sciences were developed taking from the past knowledge (re-birth of mainly Greek and Roman and some Asian knowledge) and regiven new impetus with brand new discoveries and invetions in all fields. It happened mainly in Italy because the two superpowers (grossly France and Germany, in their contemporary look, were too busy in their struggle for dominace of the continent). That the moors look like victims is like saying that a country cannot defend itself from forced occupation. I have no time to enter the Inquisition topic, but there as well much is biased with the eye of an unscholarly person who looks at History with our modern eyes and not with those who lived in that time.

  24. Murray says:

    Now, Allessandro, let me get this straight.

    It was OK for the Spanish to invade central and south America (and many other places), plunder them of gold and other valuables, torture and kill those who they couldn’t convert, destroy cultures and generally behave abominably – and it was not OK for the Moors to invade southern Spain and bring with them a thirst for knowledge (while the Christian Church violently suppressed scientists) and a generally well-ordered society?

    Don’t get me wrong here – forced occupation is wrong in most instances and I certainly don’t regard the Muslim conquests as a Good Thing by any means. But the tolerance the Moors showed for other religions and other points of view was arguably greater than the intolerance shown by the Europeans to anyone who got in their way.

    And if, as you say, the Moors just took with them the knowledge of the Greeks and the Indians, that was way better than the Dark Ages that Europe had descended into.

  25. Alan H says:

    Hi I to have just come across this site by accident
    but was searching for more information on the Moors
    and Moorish History I have watched several moor teachers
    via utube clips one Moor lecturer mentioned that the Moon
    goes around the earth 13 time a year and that the earth
    goes around the Sun 12 times a year ok yes it sounds a little strange does any one hear now or understand who
    and why this moors teacher is teaching this and could it possibily be true Yes I keep a open mind but this has go me stumped

    Regards Alan from Australia

  26. Murray says:

    Hello Alan. Please tell us the YouTube link so we can evaluate this.

  27. Hesed says:

    As it always was, the Albion can not bear to admit to the source of his establishment amongst the family of Nations, why that would mean the reason for slavery would be justified, the old wiping of the mind. Nowadays I smile, great article, typical discussion. @ Shaluh Kufu EL, ever heard of casting jewels apon swine? Lets no longer bother with the debatable.
    Lets end it like this
    WHITEHOUSE – CASA BLANCA Eastern government goes West Doh. \
    Peace.