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In page from Indian history, zero’s oldest living ancestor reveals its age

‘We now know that it was mathematicians in India in 200-400 CE who planted the seed of the idea that’d become so fundamental to modern world’

Written by Kabir Firaque | New Delhi | Updated: September 19, 2017 6:24:53 am
zero, history of zero, origin of zero, bakhshali manuscript, Brahmasphutasiddhanta, history of mathematics, zero, brahmagupta, ancient history mathematics,  arithmetic algorithms Folio 16v (228-343 AD) of the Bakhshali Manuscript shows the use of the dot as a placeholder in the bottom line. Bodleian Libraries, University of Oxford

Last week, the University of Oxford’s Bodleian Libraries announced that carbon-dating of an ancient Indian document, called the Bakhshali Manuscript, has established that it is “the world’s oldest recorded origin of the zero symbol that we use today”.

The announcement needs to be read in the context of what is already known about how the concept of zero developed in India. The manuscript, parts of which are now dated to the 3rd or 4th century AD, cannot claim to contain the earliest use of zero, a fact stressed by an Oxford professor himself.

But it does lay claim to being the oldest surviving document that expresses zero, the placeholder, in a form that would later evolve into the modern symbol for zero, the number.

For the latter concept, the credit remains with Brahmagupta, who wrote of zero as a number in Brahmasphutasiddhanta (c. 628), a few centuries after the Bakhshali Manuscript.

The manuscript

Consisting of 70 fragile leaves of birch bark, the manuscript was found buried in a field in Bakhshali village near Peshawar in 1881. From the farmer who unearthed it, it was acquired by a scholar, who presented it to the Bodleian Library in 1902.

The manuscript contains hundreds of zeros — each of which is represented by a dot and serves as a placeholder, meaning it denotes 10s, 100s or 1,000s. That in itself is not a first: other ancient civilisations too used symbols to denote zero as a placeholder, including the Babylonians 5,000 years ago, millennia before the Bakhshali Manuscript.

“But why it is so exciting is that this zero used in India, represented by a dot, is the seed from which the concept of zero as a number in its own right emerged some centuries later, something many regard as one of the great moments in the history of mathematics,” writes Marcus du Sautoy, Oxford professor of mathematics, in a discussion released with the research statement.

“In other words, it was the dot that we see in the Bakhshali Manuscript that went on to become the symbol that was first used for zero as a number in its own right.”

The manuscript’s interest to mathematicians extends beyond the zeros. In The Penguin Book of Curious and Interesting Puzzles, teacher-author David Wells describes a puzzle from the manuscript: “Twenty men, women and children earn twenty coins between them. Each man earns 3 coins, each woman 1½ coins and each child ½ coin. How many men, women and children are there?”

It is the earliest puzzle of its kind — Chinese mathematician Sun Tsuan-Ching’s version, called the ‘One Hundred Fowls’ problem, came in the 4th century.

Multiple ages

In fact, the Bakhshali Manuscript contains material from different periods. “It is actually composed of material from at least three dates, with some pages dating from as early as the 3rd to 4th century and others dating from the 8th and 10th centuries,” writes David Howell, head of heritage science at the Bodleian Libraries.

Folio 16, which contains dots representing zeros, dates from 224-383 AD, according to the radiocarbon-dating results. That makes the manuscript at least five centuries older than previously thought, the Bodleian Libraries says in a statement, referring to an earlier study by Japanese scholar Dr Hayashi Takao that had placed it between the 8th and 12th centuries.

Two periods cited by the researchers put the manuscript’s age in context. It predates not only Brahmagupta’s 7th-century magnum opus but also a 9th-century inscription in Gwalior’s Chaturbhuj Temple, so far thought to be the earliest recorded use of zero as a placeholder in India. Although Brahmagupta’s work was older than the inscription, “as far as we understand, there is no surviving document from 628, only copies. Therefore, the Gwalior temple was the oldest surviving example of the use of the symbol for zero”, Bodleian’s press manager Rosie Burke told The Indian Express in reply to a question.

The Jain text Lokavibhaga, believed to have been written in 458, was, until now, thought to contain the earliest known mention of zero as a numeral. No copies of the Prakrit original are, however, available, and even its date is derived from a later Sanskrit translation. But the Bakhshali Manuscript predates the Lokavibhaga. “We now know”, writes Professor du Sautoy, “that it was mathematicians in India in 200-400 CE who planted the seed of the idea that would become so fundamental to the modern world”.

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