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Citrabhānu’s twenty-one algebraic problems in Malayalam and Sanskrit. (English) Zbl 1326.01020

The author throws light on the Sanskrit and Malayalam versions of an early 16th-century South Indian algebraic text – Citrabhānu’s Twenty-one algebraic problems in Malayalam and Sanskrit. He mainly discusses the differences in the approaches of the two versions which includes the distinction between Sanskrit indeterminate integer remainder arithmetic techniques and Malayali fixed point iteration. Therefore, the author divides his article into four main sections, viz. (1) Introduction, (2) Sanskrit integer arithmetic vs. Malayalam fixed point iteration, (3) Other differences between the Sanskrit and the Malayalam, (4) Transmission outside India? Besides these four sections, the author presents an Appendix A entitled “Translations of the Malayalam Introduction and rules 6, 10, 17, 18, 19 and 20”.
In Section 1, he notifies the object of his paper. Section 2 is subdivided into two main themes along with a table which contains a summary of the rules in the Sanskrit and Malayalam versions. The two subdivisions are:
(i)
The Sanskrit rules: integer arithmetic. Here, the author says that the Sanskrit version aims to comply the twenty-one rules to a framework of indeterminate quotients with remainder and seems to implicitly assume as default that the unknowns should be relatively close and that remainders should be relatively small with respect to the divisor.
(ii)
The Malayalam rules: fixed point iteration. Here, the author shows that the Malayalam version is not only less committed but offers means to find the correct through fixed point iterations. He further shows that the Malayalam version is all about aviśeṣa, where the Sanskrit is strictly about indeterminate integer arithmetic with remainder.
In Section 3, the author points out that the crucial difference between the Sanskrit and Malayalam is the inclusion of proofs. In Section 4, the author speculates on the possible connections between the Twenty-one problems and the solution of cubic equation in the 16th-century Italy.
Each section is well written and well explained. The article is very useful to scholars who are going to study medieval Indian mathematics.

MSC:

01A32 History of Indian mathematics
01A40 History of mathematics in the 15th and 16th centuries, Renaissance
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
Full Text: DOI

References:

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