Why Algorithms Are Called Algorithms, and How It All Goes Back to the Medieval Persian Mathematician Muhammad al-Khwarizmi

In recent decades, a medieval Persian word has come to prominence in English and other major world languages. Many of use it on a daily basis, often while regarding the concept to which it refers as essentially mysterious. The word is algorithm, whose roots go back to the ninth century in modern-day Greater Iran. There lived a polymath by the name of Muhammad ibn Musa al-Khwarizmi, whom we now remember for his achievements in geography, astronomy, and mathematics. In that last field, he was the first to define the principles of “reducing” and “balancing” equations, a subject all of us came to know in school as algebra (a name itself descended from the Arabic al-jabr, or “completion”).

Today, a good few of us have come to resent algorithms even more than algebra. This is perhaps because algorithms are most popularly associated with the deep, unseen workings of the internet, a system with ever increasing influence over the things we do, the information we receive, and even the people with whom we associate.

Provided sufficient data about us and the lives we lead, so we’re given to understand, these algorithms can make better decisions for us than we can make for ourselves. But what exactly are they? You can get one answer from “Why Algorithms Are Called Algorithms,” the BBC Ideas video at the top of the post.

For Western civilization, al-Khwarizmi’s most important book was Concerning the Hindu Art of Reckoning, which was translated into Latin three centuries after its composition. Al-Khwarizmi’s Latinized name “Algoritmi” gave rise to the word algorismus, which at first referred to the decimal number system and much later came to mean “a set of step-by-step rules for solving a problem.” It was Enigma codebreaker Alan Turing who “worked out how, in theory, a machine could follow algorithmic instructions and solve complex mathematics. This was the birth of the computer age.” Now, much further into the computer age, algorithms “are helping us to get from A to B, driving internet searches, making recommendations of things for us to buy, watch, or share.”

The algorithm giveth, but the algorithm also taketh away — or so it sometimes feels as we make our way deeper into the twenty-first century. In the other BBC Ideas video just above, Jon Stroud makes an investigation into both the nature and the current uses of this mathematical concept. The essential job of an algorithm, as the experts explain to him, is that of processing data, these days often in large quantities and of various kinds, and increasingly with the aid of sophisticated machine-learning processes. In making or influencing choices humans would once have handled themselves, algorithms do present a risk of “de-skilling” as we come to rely on their services. We all occasionally feel gratitude for the blessings those services send our way, just as we all occasionally blame them for our dissatisfactions — making the algorithm, in other words, into a thoroughly modern deity.

Related content:

Algorithms for Big Data: A Free Course from Harvard

Advanced Algorithms: A Free Course from Harvard University

This Is Your Kids’ Brains on Internet Algorithms: A Chilling Case Study Shows What’s Wrong with the Internet Today

The Problem with Facebook: “It’s Keeping Things From You”

The Complex Geometry of Islamic Art & Design: A Short Introduction

How Youtube’s Algorithm Turned an Obscure 1980s Japanese Song Into an Enormously Popular Hit: Discover Mariya Takeuchi’s “Plastic Love”

Based in Seoul, Colin Marshall writes and broadcasts on cities, language, and culture. His projects include the Substack newsletter Books on Cities, the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.

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  • WokeLib says:

    Seriously?!! The man wrote a book crediting Hindu scholars IN THE TITLE, and you decide he “invented” it? This is cultural appropriation at its most brazen. Al-Khwarizmi was a glorified translator, and compiled knowledge from India on mathematics, astrology et al. There is no such thing as “Hindu Arabic” numerals. It’s Indian numerals which are still in use to date in India over a thousand years. Just because the West “discovered” knowledge thru middle-eastern traders doesn’t make the latter the source. Ironically, the colonialists (especially Portuguese and Brits) did a door-to-door campaign in India finding and destroying millions of ancient manuscripts because educated and scientific minded Hindu’s would not convert unless they were tortured or made ignoramuses. Job well done.

  • TurkicScholar says:

    There is no need to be enraged. As you said, Al-Khwarizmi compiled the previous knowledge of Hindu, also Hellenistic, Hebrew, and Greek treatises, with the knowledge from Arabic and Persian studies, by adding his own original findings. Such is the scientific way of progression, as european scientists also improved upon these studies. You say it like he just translated a particular book and that was all. While this is not true, we also have to accept that our current scientific progress was achieved with a lot of cultures contributing to it. Also, thanks for the great article!

  • Jonathan J Crabtree says:

    OK, let’s check the official algorithm for multiplication, which, according to dictionaries, is AB equals A added to itself B times.* Yet that would mean one multiplied by one equals two! Algorithms without common sense are useless!

    Jonathan J Crabtree
    Elementary Mathematics Historian
    Melbourne Australia

    * E.g. https://www.collinsdictionary.com/dictionary/english/multiplication

  • Moodiji says:

    Yes Indian culture is number 1. Thats why everyone wants to escape to Christian countries. The cleanliness, the attitude towards woman and cow worship are to be admired. I am Indian and the only thing I find good about Indian culture are the family values and South Indian non-veg food. You sanghs will manufacture all sorts of stories about how India was the best and all the proof was destroyed by someone else. Very convenient isn’t it.

  • Boring Geek says:

    TurkicScholar 💯. Totally agree !! Brilliantly put !! Lovely write up & lovely article too . !!

  • Super_aesthete says:

    The title of the article and the title of Al-Khwarizmi’s book are divergent.
    It is also quite illogical to attribute the discovery of algebra to him especially as he himself has documented his source.
    The Fibonnaci series is another example of misattribution. Fibonacci has documented the series as having been written by Indian mathematicians.
    We are all welcome to our illusions. But documented fact should be considered.

  • ganesh says:

    Well said. Western historians kept on lying /discredited contribution from Indians. In the history timeline, when people in the west were Nomads, Indian built super structures which are still standing today as a testimony to rich cultural ,science and technology. Request the western historians to open their eyes from Now on before uttering /peddling nonsense here!!!

  • Tulika Saha says:

    I am so glad that at least someone is bold enough to point it out. This has often been the basis of discussion (the destruction of Hindu learning and making them believe that they know nothing) in our household but I have never seen it on a public platform. Thanks for putting it out there!

  • Prad says:

    Utterly disappointed. Apparently, author has not done any research before publishing this crap.

  • subrata says:

    You might have gone through multiple orgasm after posting this? No wonder whoever feels proud about Indian culture are all sanghis … you are perhaps the one of those millions who lick the roads in USA and come back and tell us how good it feels to do that! Well done …. we don’t need you here! Next time you step into this Country, we will fix your renaming grey matter so that you can call yourself ” am white but I look little burnt”

  • ba_doh says:

    Guys … this is a post from BBC.
    Why are you all getting so worked up with it.

    If one went by BBC, India is a poor hinterland of crooks who look to Britain for moral lessons. Hehehehe. It is a comedy channel and Indians should do well to avoid watching this and helping them make money due to the bigger viewership that we offer.

    There is no point flaming on the internet with people who like the BBC (they are already brainwashed by this fake news, one sided biased channel). Just give it a pass. Get out of this question and get out of anything to do with BBC. You may think you are proving a point to other nameless faceless internet netizens … in reality you are giving popularity to this vacuous poster who quotes from the biggest media liar BBC.They make money due to this popularity. Deny them that !!!

  • Dio Brando says:

    Cringe to see Hindu nationalists raging again about another silly thing.

    The numeral system is called arabic-hindu numeral because scholars have always identified the important contributions from both cultures. The core numeral system were sourced from the Indian subcontinent which got it’s way into the persian-arabic trade. They learnt it’s more versatile than alternatives such as the Roman numerals. The persians and arabs such as Khwarizmi then improved and refined it for more complex usage and spread this knowledge to the rest of the world. Their works are further refined and improved by subsequent cultures that eventually laid the foundation of modern science.

    Today’s Hindus are the most unscientific group of people in the planet, believing in all sorts of insane conspiracies and practices. There is a weird deep rooted inferiority complex in their culture in the last decade (at least that’s when I noticed). It’s those who distance themselves away from their religious superstitions, and merely use religion as inspiration for science that contribute to the world.

    Science is a timeless art of give and take of knowledge. The genius Arab and Indian scholars of medieval times have more in common with each other and modern scientists across the world than present day useless religious nationalists.

  • Truth seeker says:

    What to say a lot. But i am tired of such low life content creators to waste my breath on them anymore.
    ALgebra and trigonometry and many more scientific advancements where done by the hindus of India. Period.

  • BELLA says:

    I don’t know why some people is acting and putting there point here everybody knows about the history and respect it as well ,so its a good thing if people are writing is down for y’all, Al-Khwarizmi brother you done really nice work , keep it up .

  • Sanghi says:

    leftist pig spotted!

  • Egalitarian says:

    Does it really matter who came up with it? They were, just like the rest of us, human. Right? Nationalism is a cancerous outgrowth from tribalism. Perhaps this was necessary at one point for our survival, after all cooperation is usually a good thing, but as soon as we create borders and territories to fight over we all lose. The internet makes the world smaller and smaller every day, so perhaps now would be a good time to consign this pathetic bickering to our past and take the acheivements of these great people and actually make them mean something, so that in another thousand years from now we can celebrate their achievements as a species that didn’t wipe itself out with its own stupidity.

  • ibrahim says:

    you never gave any evidence to support this. You said AlKhawarizmi noted his source but you never provided it and then gave an irrelevant example.

    provide some proof insead of waffle and doubt.

    Documented facts should be considered please provide some

  • Ex-Mathematician says:

    Jonathan, I think you will find that the definition of the algorithm for multiplication (AB) that you supplied there is incorrect. But maybe you knew that?
    Try adding A to itself (B-1) times (since A is already present in the result once).
    Common sense (and knowledge) applied.

    I’ve written an algorithm or two in the past, but now largely resist the temptation to.
    And they weren’t useless, or I wouldn’t have bothered.

  • Lizard says:

    Wait until you find out that air and water are both Halal.
    Your bigotry will be off the charts.

  • Lizard says:


  • Steve Douglas says:

    Yes. The definition of multiplication in that dictionary is definitely wrong – which is pretty poor. As someone else pointed out, a better version is to add A to itself (b-1) times, which still works only for positive non-zero multipliers, since you can’t add A to itself a negative number of times to multiply by less than one.

    What it really means is: If B is negative then invert the sign of both A and B. Then start with zero and add A to it B times.

    This is the sort of thing you have to do when you need to work on tiny microprocessors that have no multiply instruction – which are rare these days but do exist. There are of course, optimised ways of doing it which are faster, but that does at least work.

    Designing algorithms is rarely as straighforward as people believe, especially if you want them to work under all conditions.

  • Upananda Brahmachari. says:

    Algorithm has its definite Indian root. It can’t be denied anyway. In short, Indian Mathematics is predominantly algorithmic. In fact, the very word “Algorithm” is derived from the name of Al Khwarizmi (c. 9th Century) whose works played a crucial role in the transmission of Indian algorithmic procedures to the Islamic and later to the Western world. We shall discuss a few selected algorithms that are representative of the Indian mathematical tradition from the ancient Śulbasūtrās to the medieval texts of the Kerala School. In particular, we shall outline some of the constructions described in the Śulbasūtrās, the algorithm for computing the cube-root given by Āryabhaṭa (c.499) and the kuṭṭaka and cakraväla algorithms for solving linear and quadratic indeterminate equations as discussed by Āryabhaṭa (c.499), Brahmagupta (c.628), Jayadeva (prior to the 11th century) and Bhāskara (c.1150). We shall also discuss the efficient algorithms for accurate computation of Π and the sine function due to Mādhava (c.14th century) as discussed in the texts of the Kerala School of Mathematics and Astronomy.

  • Sutapas Bhattacharya says:

    Yes, you are correct. Henry Colebrooke showed way back in 1817 that al Khwarizmi, who translated the Indian Arithmetic (Cambridge prof. John Barrow describes the Indian Place Value Decimal Number System as the greatest ever human invention) also translated Indian Astronomical texts which utilized the Ancient Indian Algebra known as Bijaganita. Colebrooke showed how the Indian Algebra was far more advanced than anything the Greeks [who made little advance on Babylonian algebra until the late work of Diophantus] had managed. Greek mathemtics was characterized by static Geometry. Christian Yates has an article in The Conversation online entitled Five Ways Ancient India Changed the World with Maths. Modern Arithmetic, Algebra, Trigonometry and even Calculus – which laid the true foundations for the Scientific Revolution [as Charles Seife shows in Zero] were all derived from Ancient Indian mathematics.

  • Unknown says:

    This article is factually incorrect and shows the systemic bias of eurocentric goons to avoid giving any credit to India. Algorithms, decimal number systems, Algebra (including solving quadratic equations), trignometry and series approximations and even the concept of infinity were all invented by Indian (Hindu) mathematecians. Al-khwarizmi was just a translator.

  • national gallery says:

    You live and learn. I had thought the word algorithm arose as a suitable general term for the process that was common to computer programming. In so far as the latter is a means of producing an accelerated solution, it bore an obvious relation to the earlier use of the logarithm which had enabled an increased productivity in calculation. And it was probably considered to additionally suitably allude to the origination of the electronic computer.

  • Sutapas Bhattacharya says:

    Such false Eurocentric presentations are common in History and Philosophy of Science linked to so-called Western ‘Classics’. Ancient Greek shamans and mystics such as Pythagoras, Parmenides, Empedocles and Heraclitus are presented as ‘scientists’ whereas Oriental philosophers are reduced to mystical poets! Although there were exceptionas such as Colebrooke, this was linked to the British colonial looting of India. Max Muller wrote that, were he a German, Colebrooke would be celebrated throughout German academia but in England, not one word!
    It was James Mill {Father of John Stuart Mill], who started trying to decontaminate Plato of Mystical [supposedly ‘Oriental’] ‘contamination – when in fact Plato’s Philosophia was a Yoga-like practice for attaining Enlightenment (Sophia was the Cosmic Light of Wisdom). Mill who never visited India, claimed in his so-called ‘History’ that it was a Land of Eternal Poverty and Famine. He blamed this misery on Hinduism/Brahmanism which supposedly had remained unchenged for 3,000 yrs. This was to cover up the Crimes Against Humanity of his colleagues in the E India Company – who started the British imperial looting of US$45 Trillion from India [along with its deindustrialization and pauperization – see Jason Hickel’s article on Al Jazeera online – which also shows how the British lie about this] and the killing of tens of millions by exporting India’s foodgrains for British Food Security and profit. Mill rose to No2 in the EIC. This included the creation of Death Camps for victims of the 1877 Madras Famine which gave less starvation rations than Buchenwald for hard labour, killing 94% of inmates.
    In reality, in 1616 English Ambassador Thomas Roe described Delhi as the Treasury of the world and Mughal India had over 25% of global GDP. In 1877 Cornelius Walford showed that there were 30 famines in just 120 yrs in British-occupied India compared to just 17 famines in the whole of India in the previous 2,000 years.This was because native rulers acted to prevent and alleviate famines whereas the British created them with their pseudo-Free Market Social Darwinism [even denying charitable aid for the victims], exporting food and letting the poor die as also in Ireland. Thomas Malthus worked at Hailebury the EIC College. George Orwell wrote in The Road to Wigan Pier that 100 million Indians must be forced to the edge of starvation so that the British can live as they do.
    This myth about al-Khwarizmi supposedly inventing what was actually Indian maths was recently peddled on a BBC online magazine and I pointed it out but they keep deflecting by saying that his work was nonetheless important – which is sidestepping the real issue. When it comes to other forms of so-called ‘cultural appropriation the Liberal/Leftist BBC would be running around in rings apologizing to Muslims and African-origin people. I have noticed the insidious influence of Anglo-Iraqi Surrey Physics professor and TV presenter Jim al-Khalili in perpetuating such Islamic misappropriation of Indian achievements. In his TV documentaries he claimed the Indian Number system and Zero as Islam’s greatest contributions to Science. An Islamic exhibition at the London Science Museum also claimed the Zero as originating in Islamic culture. There is an Arabic propaganda film starring Ben Kingsley called 1001 Inventions which makes numerous such false claims based on absurd arguments as debunked on YT videos.

  • Sutapas Bhattacharya says:

    National Gallery – No – the English word Algorithm was used in the Middle Ages by Chaucer etc. and originally referred to the Indian Decimal Place Value Number System which al Khwarizmi translated into Arabic – and was later translated from Arabic into Latin by Leonardo of Pisa (Fibonacci).
    As I have stated in an earlier comment, Greek Maths was characterized by static Geometry [as with their static view of the universe]. Conversely, as another commenter states, Indian Maths was characteristically Algebraic or Algorithmic – and Indian cosmology had a dynamic Process view of everything as constantly changing flux [samsara – without cease].! This is also the case with Chinese maths though it should be noted that, as famous Chinese scholar Lin Yutang wrote in The Wisdom of India and China, India was China’s teacher in so many things such as Philosophy, Grammar, Quadratic Equations, Trigonometry etc…

  • Shailesh Parekh says:

    Why do you refer to any Indian who stands up for their culture/civilization as hindu nationalist? The fact is that the home of mathematics is in India. The arabs learnt it from us and exported it to the west. Many of us feel that the great contributions made to the fundamentals of human advancement by the Indian civilization are not duly recognized and for that matter appropriated. I do not feel any sense of inferiority about my culture.
    The BBC has always had a thing against hindus simply because we dont indentify ourselves as victims and we are successful forward looking people. Like most left wing entities they are the first to apologise for muslims (anyone who plays victim) and this is an attempt by them to present islam as progresssive contributor to humanity, which unfortunately is not true. They make many such programs.
    They had nothing to say about the brutality meted out to the kashmiri hindus, but will peddle the narrative of intolerance by hindus on muslims in India.

    Have a look at this clip. Honest Arab people are able to admit this.

  • Amit Shukla says:

    Algorithms were used and narrated by Āryabhaṭa (c.499) and Brahmagupta (c.628) in India in the mathematical treatises. And are narrated in the Śulbasūtrās

    Long before the birth of Al Khwarizmi (c. 9th Century)

    It is a misrepresentation to label the person who transmits ancient Indian or ancient Chinese knowledge to Europe, as the inventor. Like saying Columbus discovered America : all the native Americans and Mayans are ciphers, only the white man is the determinant of “discovery” ?

    The world neither began nor ends in Europe.

  • Felipe says:

    I don’t see this as “common sense”. It’s pure logic:

    If it is multiplication, then the algorithm is as shown. (if-then)

    The only way that this can be (logically) wrong is a case where it is, in fact, a multiplication AND the algorithm is not as presented. You arrived 1 * 1, but 1 * x is NOT a multiplication of x, so it cannot be used to test the veracity of the claim.

    Just as you cannot add zero dollars to your account, you cannot multiply amounts by one.

    Of course, you can DEFINE a multiplication by 1, to add “orthogonality”:

    A * B equals:
    B, if A equals 1
    A added to itself B times, otherwise.

    (Note that this is still incomplete, for NUMERIC SETS)

    Just as you cannot get the number set definition of an operation from the dictionary, you cannot judge a dictionary definition of a word by its use in number sets. They are different things and this has nothing to do with common sense. At least in my opinion.

  • Deepak says:

    This is again LIE and destruction of History…if you study vedas and you know sanskrit, you will find indians had wrote literature on every field of science and life.There are many which we have even today in 21st century have not started exploring like spiritual science. Ancient Indian had mastered it. Even the person who invented nuclear weapon in ctodays worls said that he relied on indian literature for it. Ancient indians were master in all sectors like Space, science, medical, ayurved, yog, yoga, life, relife etc but lost due to invasions …

  • Dovydas says:

    I dont really see how do you come to that conclusion. Why one multiplied by one equal two? A added to itself B times – lets check. A = 1 , B = 1. So A(1) added B(1) times – which is simply one A – its 1. Where you get 2?

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