Place value and zero: the evidence

01The dated witnesses

The Jain cosmology Lokavibhaga, in its Sanskrit version, says it was copied in Shaka 380, that is 458 CE, and it writes numbers in place-value words with shunya for the empty place. Aryabhata in 499 CE states the rule that each place is ten times the one before. The first zero carved in stone in Bharat with a firm date is at the small Chaturbhuj temple on Gwalior fort: the inscription of Vikrama 933 (876 CE) records a garden 270 hastas long and a gift of 50 garlands a day, both written with a round zero.

02The Bakhshali manuscript

A farmer dug up 70 birch-bark leaves near Bakhshali, near Peshawar, in 1881. They hold arithmetic problems written with a dot for zero, and the manuscript is now in the Bodleian Library, Oxford. In 2017 the library had three leaves radiocarbon-dated and got three very different ranges, roughly 224–383, 680–779 and 885–993 CE. Several historians, including Kim Plofker, have argued that leaves of one bundle are unlikely to be centuries apart and that the oldest date may reflect old bark. The text itself is not in doubt; its exact age is.

03How it travelled

The system went east and west. A Khmer inscription from Sambor on the Mekong, dated Shaka 605 (683 CE), already writes its year with a zero. Westward, the Syrian bishop Severus Sebokht praised the nine Indian signs in 662. Al-Khwarizmi wrote a book on calculating with Indian numerals around 825; its Latin version begins “Dixit Algorismi”, from which Europe got the word algorithm. Leonardo of Pisa (Fibonacci) taught the “nine Indian figures” to Italian merchants in his Liber Abaci of 1202. Arabs and Europeans still called them Hindi numerals for centuries.

In the texts

• Lokavibhaga
• Bakhshali manuscript
• Aryabhatiya, Ganitapada 2

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