What: I want to read an English translation of the chakravala method as it was described (in Sanskrit) around 1150 CE.

Why: I want to understand how the original authors such as Bhāskara II or their near-contemporary students conducted reasoning and discourse about the ideas, including which symbolic notations they used, if any. My aim is examining how symbolic notation or natural language syntax and semantics affects the conduct and communication of mathematics.

Existing non-answers: It is easy to find explanations of the algorithm itself using modern mathematical notations, such as in the main Wikipedia article already cited. I can also find a complete 1975 paper (C.-O. Selenius) that examines in detail both the novel and substantial concepts which Bhāskara II describes, and the ways in which subsequent European authors failed to understand or appreciate them. Finally, the chakravala method is cited in a high-voted answer to a soft question in this forum about mathematicians "ahead of their time".

This is a question that contemporary search engines are somehow incapable of answering, though if anyone conjures a search query that yields an actual answer then that in itself would be an interesting tertiary illustration of how to bend the great global search graph, optimized as it is for consumer advertising, to the purposes of science.


1 Answer 1


At least three English translations can be found in works all produced between 1813 and 1817 and available through the Internet Archive (from Bijaganita - Translations):

My research in asking the question eventually led me to find that the method was described in detail in Bijaganita, the second volume of Bhāskara II's three-volume Sanskrit treatise Siddhānta Shiromani. The works above are all translations of Bijaganita / "Bija Ganita" or the Siddhānta Shiromani as a whole.


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