Bakhshali Manuscript
Encyclopedia
The Bakhshali Manuscript is an Ancient Indian
mathematical
manuscript written on birch bark
which was found near the village of Bakhshali
in 1881 in what was then the North-West Frontier Province
of British India (now Khyber Pakhtunkhwa province, in Pakistan
). It's written in Śāradā script
and in Gatha
dialect (which is a combination of the ancient Indian languages
of Sanskrit
and Prakrit
). The manuscript is incomplete, with only seventy leaves of birch bark, many of which are mere scraps. Many remain undiscovered. The Bakhshali manuscript, which is currently too fragile to be examined by scholars, is currently housed in the Bodleian Library at the University of Oxford (MS. Sansk. d. 14).
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. BC and the 3d c. AD; Ian Pearce summarizes the positions:
However, earlier scholars have tended to date it around 400 AD (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 the 7th c.
The manuscript gives various algorithm
s and techniques for a variety of problems, such as computing square root
s and dealing with negative numbers.
History of India
The history of India begins with evidence of human activity of Homo sapiens as long as 75,000 years ago, or with earlier hominids including Homo erectus from about 500,000 years ago. The Indus Valley Civilization, which spread and flourished in the northwestern part of the Indian subcontinent from...
mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
manuscript written on birch bark
Birch bark document
A birch bark document is a document written on pieces of birch bark. Such documents existed in several cultures. For instance, some Gandharan Buddhist texts have been found written on birch bark and preserved in clay jars....
which was found near the village of Bakhshali
Bakhshali
Bakhshali is a village and union council in Mardan District of Khyber-Pakhtunkhwa. It is located at 34°17'0N 72°9'0E and has an altitude of 307 metres .-History:...
in 1881 in what was then the North-West Frontier Province
North-West Frontier Province
Khyber Pakhtunkhwa , formerly known as the North-West Frontier Province and various other names, is one of the four provinces of Pakistan, located in the north-west of the country...
of British India (now Khyber Pakhtunkhwa province, in Pakistan
Pakistan
Pakistan , officially the Islamic Republic of Pakistan is a sovereign state in South Asia. It has a coastline along the Arabian Sea and the Gulf of Oman in the south and is bordered by Afghanistan and Iran in the west, India in the east and China in the far northeast. In the north, Tajikistan...
). It's written in Śāradā script
Sarada script
The Śāradā, or Sharada, script is an abugida writing system of the Brahmic family of scripts, developed around the 8th century. It was used for writing Sanskrit and Kashmiri. The Gurmukhī script was developed from Śāradā...
and in Gatha
Gatha
Gatha is a type of metered and often rhythmic poetic verse or a phrase in the ancient Indian languages of Prakrit and Sanskrit. The word is originally derived from the Sanskrit/Prakrit root gai , which means, to speak, sing, recite or extol. Hence gatha can mean either speech, verse or a song...
dialect (which is a combination of the ancient Indian languages
Linguistic history of India
Originating more than 5,000 years ago, records of the linguistic history of India began with early pictures that transformed into pictorial scripts and engravings and eventually to modern orthographies...
of Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
and Prakrit
Prakrit
Prakrit is the name for a group of Middle Indic, Indo-Aryan languages, derived from Old Indic dialects. The word itself has a flexible definition, being defined sometimes as, "original, natural, artless, normal, ordinary, usual", or "vernacular", in contrast to the literary and religious...
). The manuscript is incomplete, with only seventy leaves of birch bark, many of which are mere scraps. Many remain undiscovered. The Bakhshali manuscript, which is currently too fragile to be examined by scholars, is currently housed in the Bodleian Library at the University of Oxford (MS. Sansk. d. 14).
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. BC and the 3d c. AD; 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 HoernleAugustus HoernleDr. Augustus Rudolf Hoernle was an English Orientalist. He was born in India, the son of an Anglican priest. He attended school in Switzerland, later moving to London and studying Sanskrit under Goldstucker. He returned to India in 1865, teaching first at the Benares Hindu University and later at...
). 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 400 AD (Hoernle
Augustus Hoernle
Dr. Augustus Rudolf Hoernle was an English Orientalist. He was born in India, the son of an Anglican priest. He attended school in Switzerland, later moving to London and studying Sanskrit under Goldstucker. He returned to India in 1865, teaching first at the Benares Hindu University and later at...
, 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
Aryabhata
Aryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...
(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
Brahmagupta
Brahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta , written in 628 in Bhinmal...
in the 7th c.
The manuscript gives various algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s and techniques for a variety of problems, such as computing square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
s and dealing with negative numbers.
See also
- Bakhshali approximation
- Indian mathematicsIndian mathematicsIndian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today was first...
- Zero (number)