Where Does the Word Algorithm Come From? A Baghdad Mathematician's Name
Algorithm comes from al-Khwarizmi, a mathematician who worked in Baghdad in the ninth century. The Latin form of his name, Algoritmi, became the word. One of his books also gave us algebra.
The word algorithm comes from the name of Muhammad ibn Musa al-Khwarizmi, a mathematician who worked in Baghdad in the ninth century. His book on calculating with Hindu numerals was translated into Latin in the 12th century as Algoritmi de numero Indorum. The Latin form of his name, Algoritmi, eventually became an ordinary word.
Who was al-Khwarizmi?
Al-Khwarizmi was born around 780 and died around 850, according to Britannica. The dates are approximate, and the MacTutor History of Mathematics archive at the University of St Andrews also gives 790 as a possible birth year. His name may indicate that his family came from Khwarizm, a region south of the Aral Sea in Central Asia, though that is an inference drawn from the name itself. In English his name turns up in several spellings, such as al-Khwarizmi and al-Khwārizmī, which is one reason the link to the word algorithm is so easy to miss.
What is better established is where he worked: the House of Wisdom in Baghdad, a center of learning founded by the caliph al-Ma'mun. It was there, under the caliph's patronage, that al-Khwarizmi wrote books that would reach Europe centuries later in Latin translation.
How did a mathematician's name turn into algorithm?
One of al-Khwarizmi's books explained the Hindu number system, with the digits 1 to 9 and zero, in which the value of each digit depends on its position. It is the system we still use today. The Arabic original is lost. What survives is a 12th-century Latin version that MacTutor describes as much changed from the original text.
That Latin version opened with the author's name: Algoritmi de numero Indorum, which Britannica renders as Al-Khwarizmi Concerning the Hindu Art of Reckoning. Over time, the Latinized name stopped pointing to a person and started pointing to the method. In the Middle Ages, algorism became the name for the system of calculating with these numerals. According to Merriam-Webster, the word passed through Old French and Medieval Latin into Middle English as algorisme before reaching its modern form.
| Stage | Form | When |
|---|---|---|
| The author's name, in Arabic | al-Khwarizmi | 9th century, Baghdad |
| Title of the Latin translation | Algoritmi de numero Indorum | 12th century |
| Name for the system of reckoning | algorism (Middle English algorisme) | Middle Ages |
| A step-by-step procedure | algorithm | First known use: 1811 |
The 1811 date is the one Merriam-Webster gives for the step-by-step sense. The same dictionary says elsewhere that the word only became common in the 20th century and, until recently, was used mostly in mathematics and computing.
And where does algebra come from?
Also from al-Khwarizmi. His most famous book is titled, in the form Britannica gives, Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala, or The Compendious Book on Calculation by Completion and Balancing. The word al-jabr in the title became algebra.
According to MacTutor, al-jabr means completion: the operation of removing negative terms from an equation. A modern example, just to illustrate: in x − 3 = 7, adding 3 to both sides completes the equation and leaves x = 10. Al-muqabala, balancing, is the operation of cancelling like terms on both sides. A single author, then, gave the world two words every student knows.
So what exactly is an algorithm?
Today, an algorithm is any finite sequence of well-defined steps for solving a problem. The long division and column addition taught in school, worked out digit by digit with 0 through 9, are algorithms in the oldest sense: rules for calculating with the positional system al-Khwarizmi's book described.
Modern algorithms do far more complex things. They are how a receiver works out its position from GPS satellite signals, how search engines rank results and how social networks choose what shows up on your screen. Many of today's robots, a word born in a Czech play, are nothing more than algorithms at work.
Why is his name so little known?
Partly because, in Europe, the name arrived in disguise. Medieval readers knew the author as Algoritmi, and the word drifted away from the man until it looked like any other technical term. Algorithm isn't the only everyday word with a foot in Arabic: the Spanish name for the @ sign, arroba, is another example of how vocabulary preserves old routes of trade and learning.
The next time someone says the algorithm decided what shows up on your phone, remember that, quite literally, they are naming a Baghdad scholar who wrote about arithmetic more than a thousand years ago.
