Bakhshali (Pakistan): Indian Manuscript Contains Oldest Example of Mathematical Symbol ‘Zero’

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The Bakhshali manuscript, an ancient Indian mathematical manuscript written on more than 70 leaves of birch bark, is notable for having a dot representing ‘zero’ in it. The date of the manuscript has intrigued scientists for years, with many believing it dated from the 9th century CE. Now researchers from the University of Oxford and the Bodleian Libraries have carbon dated the manuscript and found that it dates from between the 3rd and 4th centuries CE, making it the world’s oldest recorded origin of the zero symbol that we use today.

Image 5231 1 bakhshali manuscriptThe Bakhshali manuscript contains the oldest recorded example of the symbol that we use for zero today. The 70 leaves of birch bark that make up the manuscript are incredibly fragile and are housed in this specially designed book at the Bodleian Libraries’ Weston Library, Oxford. Scholars are able to view both sides of the birch bark through the ‘windows’ of the book. Image credit: Bodleian Libraries, University of Oxford.

The Bakhshali manuscript was found in 1881 by a farmer in his field in Bakhshali (near modern Peshawar, Pakistan).

The manuscript is a compendium of rules and illustrative examples. It gives the solutions of the most of the examples together with their verification, and contains material relating to arithmetic, algebra, and geometry.

The topics include fractions, square-root, arithmetical and geometrical progressions, income and expenditure, profit and loss, computation of gold, interest, rule of three, summation of certain complex series, simple equations, simultaneous linear equations, quadratic equations, indeterminate equations of the second degree of a particular type, mensuration and miscellaneous problems.

Written in a variant of Buddhist Hybrid Sanskrit, the Bakhshali manuscript is broadly recognized as the oldest Indian mathematical text, however, the exact age of the text is widely contested.

The surprising results of the first ever radiocarbon dating conducted on this manuscript reveal that it dates from as early as the 3rd or 4th century. This means that it in fact predates a 9th-century inscription of zero on the wall of a temple in Gwalior, Madhya Pradesh, which was previously considered to be the oldest recorded example of a zero used as a placeholder in India.

Image 5231 2 bakhshali manuscriptCarbon dating has revealed that folio 16 from the 70-page Bakhshali manuscript dates from 224-383 CE. You can see the use of a dot as a placeholder in the bottom line. Image credit: Bodleian Libraries, University of Oxford.

The zero symbol that we use today evolved from a dot that was used in ancient India and can be seen throughout the Bakhshali manuscript,” said University of Oxford Professor Marcus du Sautoy and co-authors.

The dot was originally used as a ‘placeholder,’ meaning it was used to indicate orders of magnitude in a number system — for example, denoting 10s, 100s and 1000s.”

While the use of zero as a placeholder was seen in several different ancient cultures, such as among the ancient Mayans and Babylonians, the symbol in the Bakhshali manuscript is particularly significant for two reasons.

Firstly, it is this dot that evolved to have a hollow center. Secondly, it was only in India that this zero developed into a number in its own right, hence creating the concept and the number zero that we understand today — this happened in 628 CE when the Indian astronomer and mathematician Brahmagupta wrote a text called Brahmasphutasiddhanta, which is the first document to discuss zero as a number.

Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world,” Professor du Sautoy said.

But the creation of zero as a number in its own right was one of the greatest breakthroughs in the history of mathematics.”

We now know that it was as early as the 3rd century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics has been in the Indian sub-continent for centuries.”

Determining the date of the Bakhshali manuscript is of vital importance to the history of mathematics and the study of early South Asian culture and these surprising research results testify to the subcontinent’s rich and longstanding scientific tradition,” said Richard Ovenden, Bodley’s Librarian.