Last month, the Bodleian Library at Oxford University announced that a Sanskrit manuscript housed in the library for the last century had been dated using radiocarbon techniques. Oxford's radiocarbon dating laboratory announced that the three of the birch-bark folios of the Bakhshali Manuscript could be dated to roughly CE, CE and CE. The key result was, the library said, that one of the manuscript's leaves contained the oldest known written zero. The library also announced that the zero in the manuscript was not a "true" zero, in the sense that it functioned only as a marker showing an empty decimal place, and not as a fully-fledged number that participates in calculations. The team, which includes scholars from universities in the USA, France, Japan, New Zealand and the University of Alberta in Canada, has published a peer-reviewed article that refutes several of the Library's key assertions.
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The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in in the village of Bakhshali , Mardan near Peshawar in present-day Pakistan. It is perhaps "the oldest extant manuscript in Indian mathematics.
The manuscript contains the earliest known Indian use of a zero symbol. The manuscript was unearthed from a field in ,  by a peasant in the village of Bakhshali , which is near Mardan , now in Khyber Pakhtunkhwa , Pakistan. Kaye, who edited the work and published it as a book in The extant manuscript is incomplete, consisting of seventy leaves of birch bark ,   whose intended order is not known. The manuscript is a compendium of rules and illustrative examples.
Each example is stated as a problem, the solution is described, and it is verified that the problem has been solved. The sample problems are in verse and the commentary is in prose associated with calculations. The problems involve arithmetic , algebra and geometry , including mensuration.
The topics covered include fractions, square roots, arithmetic and geometric progressions , solutions of simple equations, simultaneous linear equations , quadratic equations and indeterminate equations of the second degree. The brahmin might have been the author of the commentary as well as the scribe of the manuscript. The manuscript is a compilation of mathematical rules and examples in verse , and prose commentaries on these verses.
The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers profit and loss , measurement such as of the fineness of gold, etc.
Scholar Takao Hayashi has compared the text of the manuscript with several Sanskrit texts. He discusses similar passages in Ramayana , Vayupurana , Lokaprakasha of Kshemendra etc. An unnamed manuscript, later than Thakkar Pheru , in the Patan Jain library, a compilation of mathematical rules from various sources resembles the Bakhshali manuscript, contains data in an example which are strikingly similar.
The Bakhshali manuscript uses numerals with a place-value system, using a dot as a place holder for zero. References to the concept are found in Subandhu's Vasavadatta , which has been dated between and by the scholar Maan Singh. Prior to the carbon dating — which, however, has in the meantime been discounted, see below under Date — a 9th-century inscription of zero on the wall of a temple in Gwalior , Madhya Pradesh, was thought to be the oldest Indian use of a zero symbol.
In , three samples from the manuscript were thought to come from three different centuries, from AD —, —, and —, on the basis of a study involving radiocarbon dating. If the dates were accepted, it is not known how fragments from different centuries came to be packaged together.
A detailed reconsideration of all relevant evidence regarding the date of the Bakhshali manuscript, led Kim Plofker, Agathe Keller, Takao Hayashi, Clemency Montelle and Dominik Wujastyk to conclude the following: "We express regret that the Bodleian Library kept their carbon-dating findings embargoed for many months, and then chose a newspaper press-release and YouTube as media for a first communication of these technical and historical matters.
The Library thus bypassed standard academic channels that would have permitted serious collegial discussion and peer review prior to public announcements. It should not be hastily assumed that the apparent implications of results from physical tests must be valid even if the conclusions they suggest appear historically absurd. Referring to the detailed reconsideration of the evidence by Kim Plofker et al. Among the variables of carbon dates, variation in script and linguistic variation, the first is the most objective but still much in need of calibration for relatively recent, historical dates.
Prior to the proposed radiocarbon dates of the study, most scholars agreed that the physical manuscript was a copy of a more ancient text, whose date had to be estimated partly on the basis of its content. Datta assigned it to the "early centuries of the Christian era". Also writing is a normative activity and moreover dependent on some amount of individual variation from scribe to scribe.
Other evidence, including the laboratory results of radiocarbon dating, is to be interpreted in the light of the results reached by careful palaeographic study.
From Wikipedia, the free encyclopedia. This section contains too many or overly lengthy quotations for an encyclopedic entry.
Please help improve the article by presenting facts as a neutrally worded summary with appropriate citations. Consider transferring direct quotations to Wikiquote. December Hoernle , p. Kaye, on the other hand, thought in that the work was composed in the 12th century,   but this was discounted in recent scholarship. Joseph wrote, "It is particularly unfortunate that Kaye is still quoted as an authority on Indian mathematics.
OPLI — Vol. The Guardian. Retrieved Bodleian Library. Oxford University Press. Hayashi , p. The MacTutor History of Mathematics archive. School of Archaeology, University of Oxford. Archived from the original on Robinson May Archived from the original on 9 August Indian mathematics. Bibhutibhushan Datta T. Sarasvati Amma A. Walter Eugene Clark David Pingree. Babylon China Greece Islamic mathematics Europe. Namespaces Article Talk. Views Read Edit View history.
Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'
Nowt, nada, zilch: there is nothing new about nothingness. But the moment that the absence of stuff became zero, a number in its own right, is regarded as one of the greatest breakthroughs in the history of mathematics. Now scientists have traced the origins of this conceptual leap to an ancient Indian text, known as the Bakhshali manuscript — a text which has been housed in the UK since Radiocarbon dating reveals the fragmentary text, which is inscribed on 70 pieces of birch bark and contains hundreds of zeroes, dates to as early as the 3rd or 4th century — about years older than scholars previously believed. The Bakhshali manuscript was found in , buried in a field in a village called Bakhshali, near Peshawar, in what is now a region of Pakistan.
The Bakhshali Manuscript and the Indian Zero
The origin of the symbol zero has long been one of the world's greatest mathematical mysteries. This means that the manuscript 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. The findings are highly significant for the study of the early history of mathematics. 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. 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 centre and became the symbol that we use as zero today. Although the Bakhshali manuscript is widely acknowledged as the oldest Indian mathematical text, the exact age of the manuscript has long been the subject of academic debate.