The Bakhshali Manuscript

An extract on the Bakhshali Manuscript from Rohini Chowdhury's upcoming book on Indian Mathematics:

"Probably written during the 3rd or 4th century AD, it is a manual on the mathematics of ancient India and contains mathematical rules, example problems and their solutions. Only a small part of the original manuscript survives; this deals mainly with algebra and arithmetic, with some problems on geometry and mensuration. We do not know what the missing portions of the Manuscript contained. Since the beginning and end of the Manuscript are missing, we also do not know what the work was called or who wrote it. Nevertheless it is a critical find, and provides a bridge between the mathematics of the ancient and the Classical era. It is also unique in that this is the first time we see mathematics in ancient India free from religious associations or philosophical considerations. The Bakhshali Manuscript deals with mathematics, and mathematics alone.

It is written in the Sharada script, and zero is represented by a dot.

There has been intense debate amongst historians and scholars regarding the date of this manuscript. After a detailed analysis of the contents of the manuscript – including the language in which it is written, the currency mentioned in several of the problems, the terminology used, and the absence of certain mathematical techniques which were known to have been in use by the 5th century AD – scholars and historians have concluded that while the physical manuscript dates back to the 8th century AD, it is a copy of a much older work which was probably composed sometime during the 3rd or 4th centuries AD. These dates place the contents of the Bakhshali Manuscript before the classical period which begins approximately around 500 AD with the work of the great mathematician Aryabhata.

The precise dating of the manuscript is important from the point of view of discussing the developments in ancient Indian mathematics. If the above dates are accepted, they make the Bakhshali Manuscript roughly contemporary to the Lokavibhaga .....This makes sense, especially from the point of view of the invention of the place-value system which is used throughout the manuscript. Some scholars suggest that given the period in which it was probably first written, the Bakhshali Manuscript could have been the work of Jain monks, but there is no evidence to support this view."

Image:
A leaf from a birch bark manuscript that was discovered in 1881 by a farmer while digging a field about fifty miles from modern Peshawar in Pakistan. The text is a collection of algorithms and sample problems in verse, with a commentary explaining them in a combination of prose and numerical notation. It provides unique evidence for how medieval Indian mathematics was written in manuscript. Numerals are expressed in decimal place form and the zero is represented by a round dot. Quantities are expressed in numerals set off from the text by horizontal and vertical boxes. Fractions are written in the familiar way, but with no line dividing numerator and denominator, and negative values are shown by a small cross after the number, similar to the modern ‘+’ sign.

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