Where our numbers came from

One lazy afternoon Reema was flipping through an old book when a piece of paper slipped out, covered in strange symbols. Her father smiled: about 4000 years ago a civilisation flourished in Mesopotamia, in western Asia (much of present-day Iraq and some neighbouring countries), and this was one of the ways they wrote numbers.

Her questions came in a rush. Since when have people been counting? What were they counting? And since when have they written numbers the way we do?

Counting is as old as the Stone Age. People counted the food they had, the animals in their herds, goods in trade and offerings at rituals; and they kept track of the days, to know when the new moon, the full moon or a new season would come.

Our way of naming numbers began in India. Ancient texts such as the Yajurveda Saṁhitā already list names for numbers by powers of 10, almost as we say them today: eka, dasha, shata, sahasra, āyuta, running all the way up to 10¹² and beyond.

The way we write them, with the digits 0 to 9, was also developed in India, about 2000 years ago. The first known use of ten digits including a 0 (then written as a dot) is in the Bakhshali manuscript, from around the 3rd century CE. Aryabhata, around 499 CE, was the first to fully explain the system and do big scientific calculations with it.

From India the system reached the Arab world by about 800 CE. It was made popular there by the Persian mathematician Al-Khwārizmī, whose name gives us the word 'algorithm', in his book On the Calculation with Hindu Numerals (c. 825), and by the philosopher Al-Kindi in On the Use of the Hindu Numerals (c. 830).

From there it reached Europe and parts of Africa by about 1100 CE, and around 1200 the Italian mathematician Fibonacci argued hard for it. Even so, Roman numerals were so deeply rooted in Europe that the change took centuries more; only by the 17th century had it become impossible to do science without the new numbers.

Laplace put it best: 'The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated.'

A note on the name. Europeans met these numerals through the Arab world, so they called them 'Arabic numerals'; Arab scholars themselves called them 'Hindu numerals'. Today they are called Hindu, Indian or Hindu-Arabic numerals, and here 'Hindu' means a place and a people, not a religion.