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Mathematical Treasure: Bakhshali Manuscript

Frank J. Swetz (The Pennsylvania State University)

In 1881, a mathematical manuscript written on birch bark was uncovered near the Indian village of Bakhshali. Named after this village, the Bakhshali Manuscript is the oldest, extant mathematical document from India. An accompanying Sanskrit inscription notes that it was

Written by the son of Chajaka, a brahmana and king of mathematicians ....

Written in Sanskrit, the manuscript is a collection of computational, arithmetical, and algebraic algorithms and simple problems. The dating of its origin is controversial and ranges from the second century CE to the tenth century CE, with some consensus that the manuscript is a later copy (8th to 10th century CE) of an earlier original (2nd century BCE to 5th century CE). This image of one leaf of the manuscript is presented courtesy of the Bodleian Library, Oxford University, which holds all known remnants of the manuscript.

Editors’ Note: For developments in the dating of this manuscript that emerged after this Mathematical Treasure was prepared, see Indian Zeros in Convergence.


J. J. O'Connor and E. F. Robertson, Bakhshali Manuscript, MacTutor History of Mathematics Archive, 2000

Ian Pearce, Bakhshali Manuscript, MacTutor History of Mathematics Archive, 2002

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Bakhshali Manuscript," Convergence (October 2015)