Hindu-Arabic numerals head west

The story

Ten signs to write every number

Every day we write numbers with ten signs: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. With these, in endless combinations, you can write any number, huge or tiny. It seems normal to us, but it is a brilliant invention, born in India. The decisive idea is that the value of a digit depends on the place where it stands: in the number 505 the first 5 is worth five hundred and the last one five. And if in a place there is nothing, you need a sign to show “nothing”: the zero.

In India this system had been in use for a few centuries. A mathematician and astronomer, Brahmagupta, wrote down in a book in 628 the rules for calculating with zero as if it were a number in every respect: he explained what happens when you add, subtract or multiply by zero. It was an absolute novelty, which no other people had yet explained so clearly.

Words travel too. The Arabs called zero “sifr”, which means “empty”. When the word reached Italy, in the Middle Ages, it became “zefiro” and then “zero”; from the same “sifr”, with another meaning, the word “cipher” also derives. So an Arabic word reminds us that those signs came from far away.

Baghdad and the House of Wisdom

At the beginning of the 9th century the capital of the Abbasid caliphate, Baghdad, was the most learned city in the world. The caliphs, in particular al-Mansur and al-Ma'mun, had Greek, Persian and Indian books translated into Arabic. The centre of this work was the “House of Wisdom”, a library and place of study where translators and scientists worked, including Christians and Jews.

One of them was Muhammad ibn Musa al-Khwarizmi, born in Central Asia around 780. He studied Indian and Greek texts, and around 825 he wrote a book on calculating with Indian numerals, which explained how to do additions, subtractions, multiplications and divisions with those ten signs. The Arabic original has been lost, but a Latin translation of the 12th century survives, which begins with the words “Dixit Algorizmi”, that is, “Al-Khwarizmi said”. This is where the word “algorithm” comes from, which today is used for a sequence of instructions, for example in a computer program.

Al-Khwarizmi also wrote another book, “The Compendious Book on Calculation by Completion and Balancing” (about 820), which taught how to solve equations, that is, problems with an unknown number. The Arabic word for “completion”, al-jabr, gave us the word “algebra”.

The long journey to Europe

The Indian numerals spread throughout the Islamic world, from Baghdad to Spain, and changed: the shapes of the signs varied from country to country, and the ones used in the West, called “ghubar” (dust), are the ancestors of ours. In Christian Europe, for a few centuries, the new numerals were known to very few scholars. The oldest Spanish manuscript that shows them dates from 976 (without the zero). A great scholar, Gerbert of Aurillac, who had studied in Catalonia and who in 999 became pope as Sylvester II, made the numerals known, used on the abacus and without the zero.

For mass use, people had to wait. In 1202 the Pisan merchant Leonardo Fibonacci, who had learned the system in Algeria, wrote the “Liber abaci” to teach it to Europeans. Even then, calculations were still mostly done with the abacus and with Roman numerals, and the new system took hold slowly, with the help of merchants and later of printing.

That is why today we call them “Arabic numerals”, because it was the Arabs who brought them to Europe, but more precisely they are “Hindu–Arabic”.