The Bakhshali Manuscript: Archaeological Evidence

The ancient birch-bark manuscript that rewrote zero's history

Explore the Bakhshali manuscript discovered in 1881, containing some of the earliest written zeros, and the debate over its dating.

The Farmer's Spade

In the summer of 1881, in a field near the village of Bakhshali in the Yusufzai subdivision of Peshawar District, a tenant farmer struck a small stone enclosure while digging. Inside, protected from the elements by the earth and the stone, lay a stack of roughly seventy folios of birch bark, brittle with age and covered in a script he could not read. He had no way of knowing he had just uncovered the earliest surviving mathematical manuscript from early India.

He took the bundle to his local revenue officer, who passed it to the Assistant Commissioner at Mardan, who forwarded it through Major-General A.A. Tregear to Rudolf Hoernle at the Indian Museum in Calcutta. Hoernle read Sanskrit. He read Śāradā. The first time he looked carefully at the pages, he understood that he was holding something nobody had expected to find: a mathematical manuscript from early India, written in verse, worked through with examples, and, on page after page, using a single dot to mean 'there is no digit here'.

This lesson is about that dot.

What the Manuscript Actually Contains

The Bakhshali Manuscript, now preserved at the Bodleian Library in Oxford under shelfmark MS. Sansk. d. 14, is a practical handbook. It teaches arithmetic and early algebra by working through problems. There are merchants dividing profits. There are soldiers sharing rations. There are systems for extracting square roots by iteration, using a formula so accurate that modern historians have compared it to the Newton-Raphson method a thousand years early. There are solutions to linear equations, and rules for handling fractions.

What sets the manuscript apart, though, is not the problems it solves. It is how it writes its answers. When a digit is missing, the scribe writes a dot. This dot, called bindu in Sanskrit, is the direct physical ancestor of the circle we now use for zero. The dot is not only a placeholder. It appears as a standalone quantity in the middle of calculations. The scribes were doing, on birch bark, what Brahmagupta would later formalize in rules. They were computing with nothing, and they were doing it casually, without any sense that the operation required defence.