Where does the word "algorithm" come from, and who gave rise to it?

Every evening the cashier Dilnoza does the same thing: she counts the money in the till, works out the total of the day's receipts, compares the two, and if there is a difference she writes down the reason. Four steps, always in the same order. Even if she does not know it, this is an algorithm. And the word itself is left over from the name of a man from Khwarazm who lived about twelve centuries ago.

Who was al-Khwarizmi?

Muhammad ibn Musa al-Khwarizmi was a mathematician and astronomer who was born around 780 and died around 850. His nisba shows his connection with Khwarazm: "al-Khwarizmi" means "from Khwarazm". Historians believe that he or his ancestors came from this land; today the region is part of Uzbekistan and Turkmenistan.

According to Britannica, he worked in Baghdad, in the time of the caliph al-Ma'mun, at the Bayt al-Hikma ("House of Wisdom"). Britannica describes this institution as the palace library of the Abbasid caliphs and writes that its heyday fell in the reign of al-Ma'mun (813–833).

How did a name become a word?

Al-Khwarizmi wrote a book on calculating with Hindu numerals. Its Arabic original has not come down to us, but a Latin translation made in the 12th century has survived. The manuscript in Cambridge University Library begins with the words "Dixit Algorizmi", "Algorizmi said". The famous title "Algoritmi de numero Indorum" ("Algoritmi on the Hindu numbers") was given by the Italian scholar Baldassarre Boncompagni, who published the manuscript in Rome in 1857; some historians regard this title as conventional and prefer to call the work by its opening words.

The chain that followed was roughly this:

According to a University of Melbourne publication, the word acquired its present broad meaning only in the 20th century, with the development of computing machines and computer science. So the honest answer to the question "who gave rise to the algorithm?" is this: al-Khwarizmi's name gave rise to the word, while the idea of step-by-step calculation is even older. Al-Khwarizmi's merit is that his books explained calculation as a sequence of precise rules, and this approach passed into Europe.

What did Hindu-Arabic numerals give the bookkeeper?

Britannica writes that al-Khwarizmi's work on arithmetic introduced Hindu-Arabic numerals and the method of calculating with them to the West in the 12th century. The power of these numerals lies in place value and zero. A single "4" sign means four, forty or four hundred depending on its position.

To feel the difference, let us look at one simple addition in two notations (an example prepared by the author):

In the right-hand column you can add in columns: units under units, tens under tens. In the left-hand column you have to group and replace the symbols every time. In a ledger with a thousand entries, this difference turns into hours of time.

The algorithm in today's accounting

An algorithm is arranging steps in a strict order so that the result comes out the same every time. An accountant does this every day. For example, with the general VAT rate of 12%, the algorithm for extracting VAT from an amount shown inclusive of VAT (hypothetical figures, prepared by the author):

1. Take the amount including VAT: 5 600 000 soum.
2. Divide it by 112: 50 000.
3. Multiply the result by 12: VAT = 600 000 soum.
4. Check: 5 600 000 − 600 000 = 5 000 000; 5 000 000 × 12% = 600 000. It matches.

The cashier Dilnoza's evening check, the month-end close in accounting software and a bank's processing of a payment are all built on this logic: a known input, precise steps, a verifiable output.

Conclusion

The name of our ancestor lives on in the word "algorithm". We do not say that he invented accounting or the computer: such a claim does not fit history. But the fact that the scholar who explained convenient rules for calculating with numerals and contributed to their spread around the world was a son of Khwarazm is reason enough for genuine pride.