Two stories, not one
The digits 0 to 9 that most of the world uses today have a long ancestry, and it helps to keep two questions apart. One is where the shapes came from. The other is where the idea of place value with a zero came from. They are related, but they are not the same story, and the evidence for each is different.
The usual short answer is that the shapes descend from the Brahmi numerals of ancient India, and that the positional system was developed in India during the first millennium CE. Scholars agree on that outline but discuss many of the details.
Brahmi numerals in early inscriptions
Brahmi is an ancient Indian script, and its earliest well-dated use is in the edicts of the emperor Ashoka in the third century BCE. Brahmi numerals appear in inscriptions of Ashoka and later in cave inscriptions of the following centuries, such as those at Nana Ghat and Nasik.
These early numerals were not a place-value system. There were separate signs for 1, 2, 3 and 4, and further signs for 5, 6, 7, 8 and 9; separate signs for the tens, such as 10, 20 and 30; and signs for 100 and 1,000. A number like 247 was written by combining signs for 200, 40 and 7, so the system was closer to an additive one than to the digits we use. The numbers 1, 2 and 3 were simple strokes, one, two and three, while 4 and later signs had distinct shapes that look quite different from their modern descendants.
The arrival of place value and zero
Somewhere in the following centuries, Indian mathematicians began using nine digit signs in positions, with a way of marking empty places. Exactly when is a matter of discussion. Sanskrit texts used a different method, writing numbers in verse with words for the digits placed in order from lowest place to highest, which already treats numbers positionally. Ancient Indian number words, such as “moon” for one or “eyes” for two, were chosen to fit the poetry.
For written signs, one early source is the Bakhshali manuscript, a birch-bark document found in what is now Pakistan, which uses a dot as an empty-place marker. Its dating is debated, with some recent radiocarbon work suggesting that parts are older than earlier estimates, but it is hard to treat any single date as settled. Among the clearest datable examples are inscriptions in which a zero appears in dated numbers. A stone inscription in Cambodia dated to 683 CE and an inscription at Gwalior in India dated 876 CE are often cited. In the early seventh century, the mathematician Brahmagupta set out rules for arithmetic with zero and negative numbers, which shows that zero was by then treated as a number and not only an empty-place marker. This is a central theme of the history of zero, and Brahmagupta’s work on negative numbers is a notable early contribution.
Gupta, Nagari and the shape changes
As Brahmi script evolved into later forms, the numerals changed with it. Gupta-period shapes, in the early centuries CE, were developments of the Brahmi ones. Later, Nagari forms emerged, ancestors of the modern Devanagari digits used for Hindi, Marathi and Nepali. At the same time, regional scripts in southern and eastern India developed their own digit shapes, so the family of Indian numerals eventually looked quite varied.
Arabic scholars take them up
Indian methods of calculation were noticed beyond India. A Syriac writer, Severus Sebokht, mentioned in the seventh century that the Indians had a method of calculation using nine signs. In the ninth century, the scholar al-Khwarizmi, working in Baghdad, wrote a text on calculation with Indian numerals that survives only in Latin translation. Other writers, such as al-Kindi, also wrote about them. These works helped to establish Indian methods in the Arabic-language world and later, through Latin translations, in Europe.
At first, Arabic mathematicians used several systems side by side. Abjad numerals, which follow the old alphabetic order, remained in use for some astronomical and everyday purposes. Over time, two families of digit shapes developed:
- Eastern forms, the so-called Arabic-Indic digits, used in much of the Middle East and other regions.
- Western forms, sometimes called ghubar or “dust” digits, used in North Africa and Islamic Spain.
The digits that reached Europe came mainly from the western Arabic-writing world. This is why European digits are commonly called “Arabic numerals” even though the Arabic-writing peoples credited India. The term Hindu-Arabic recognises both stages.
Becoming the shapes we know
The European forms continued to change. Medieval manuscripts show digits in different styles; a 4 might look like a half-open loop, a 5 might resemble a 4, and a 7 might be nearly an upside-down V. The book of 1202 known as Liber Abaci taught them to merchants, and later printing in the fifteenth century gradually made the shapes more uniform. The modern forms of 2, 3, 4 and 5 are more easily traced than 1 or 7, and any chart of the changes is best seen as a general pattern rather than a precise lineage.
What remains uncertain
Some links in the chain are still discussed by scholars. The dates of early positional use, the influence of other cultures such as China or Greece on Indian practice, and the exact paths by which certain shapes changed are all topics of continuing work. What is secure is the general sequence: Brahmi signs, an Indian positional system with zero, transmission through Arabic-language scholarship, and adoption in Europe, leading to the digits used worldwide now.