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Bakhshali Manuscript
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The Bakhshali Manuscript is a mathematical manuscript written on birch bark which was found near the village of Bakhshali in what is now Pakistan in 1881. The manuscript is incomplete, with only seventy leaves of birch bark, many mere scraps, remaining.
Its date is uncertain, and has generated considerable debate. Most scholars agree that the physical manuscript is a copy of a more ancient text, so that the dating of that ancient text is possible only based on the content.
Recent scholarship dates it between the 2nd c. BCE and the 3d c. CE; Ian Pearce summarizes the positions:
- Gurjar discusses its date in detail, and concludes it can be dated no more accurately than 'between 2nd century BC and 2nd century AD'. He offers compelling evidence by way of detailed analysis of the contents of the manuscript (originally carried out by R Hoernle). His evidence includes the language in which it was written ('died out' around 300 AD), discussion of currency found in several problems, and the absence of techniques known to have been developed by the 5th century. Further support of these dates is provided by several occurrences of terminology found only in the manuscript, (which form the basis of a paper by M Channabasappa)..
However, earlier scholars have tended to date it around 400AD (Hoernle, Datta/Singh, Bag, Gupta).
Hayashi had suggested a possible seventh century date,
while in an early colonial estimate, G.R. Kaye had assessed it to be as late as 12th c. AD. Such late dates are quite unlikely because the language used was already dying by the 4th c.; also the work does not mention integer equations and other topics which were of widespread interest after Aryabhata (5th c. AD). Today, Kaye's assessment is widely discredited..
The reason why the date of the manuscript is important, is that if the work indeed dates
from the 3d c. or earlier, it would imply that the concept of the mathematical zero was known several centuries earlier than the work of Brahmagupta in (7th c.).
The manuscript gives various algorithms and techniques for a variety of problems, such as computing square roots and dealing with negative numbers.
See also
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