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Ancient mathematical text

The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present day Pakistan, historical Gandhara). It is perhaps "the oldest extant manuscript in Indian mathematics".). The manuscript contains the earliest known Indian use of a zero symbol. It is written in a form of literary Sanskrit influenced by contemporary dialects.

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 manuscript is written in an earlier form of Sharada script, a script which is known for having been in use mainly from the 8th to the 12th century in the northwestern part of South Asia, such as Kashmir and neighbouring regions. It is possible that the manuscript might be a compilation of fragments from different works composed in a number of language varieties. Hayashi admits that some of the irregularities are due to errors by scribes or may be orthographical. A colophon to one of the sections states that it was written by a brahmin identified as "the son of Chajaka", a "king of calculators," for the use of Vasiṣṭha'''s son Hasika''. The brahmin might have been the author of the commentary as well as the scribe of the manuscript. Prior to the 2017 carbon dating, a 9th century inscription of zero on the wall of a temple in Gwalior, Madhya Pradesh, was once thought to be the oldest Indian use of a zero symbol. Referring to the detailed reconsideration of the evidence by Plofker et al., Sanskrit scholar, Jan Houben remarked:
text=''"If the finding that samples of the same manuscript would be centuries apart is not based on mistakes there are still some factors that have evidently been overlooked by the Bodleian research team: the well known divergence in exposure to cosmic radiation at different altitudes and the possible variation in background radiation due to the presence of certain minerals in exposed, mountainous rock have nowhere been taken into account." but this was discounted in recent scholarship. G. G. Joseph wrote, "It is particularly unfortunate that Kaye is still quoted as an authority on Indian mathematics." Indian scholars assigned it an earlier date. Datta assigned it to the "early centuries of the Christian era". Hayashi noted some similarities between the manuscript and Bhaskara I's work (AD 629), and said that it was "not much later than Bhaskara I".