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Dispelling mathematical doubts. Assessing the
mathematical correctness of algorithms in Bhâskara's commentary on the mathematical chapter of the Âryabhatîya.

Abstract : In his commentary on the mathematical chapter of the Âryabhatîya, a Sanskrit astronomical treatise of the fifth century, Bhâskara (629 CE) provides explanations, demonstrations and verifications to check the computational accuracy and logical consistency of some procedures. These unsystematic attempts at justification are often fragmentary and perhaps mere echoes of an activity carried out orally. Nonetheless, recurring modes of reasoning can be brought to light. To ground mathematically a procedure, a 're-interpretation' via the Rule of Three and the 'Pythagorean Theorem' could be provided. Another way of assessing the validity of a procedure was to establish an independent alternative procedure arriving at the same result.
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Agathe Keller. Dispelling mathematical doubts. Assessing the
mathematical correctness of algorithms in Bhâskara's commentary on the mathematical chapter of the Âryabhatîya.. Chemla, Karine. The History of Mathematical Proof in Ancient Traditions, Cambridge University Press, pp.487-508, 2012. ⟨halshs-00151013v4⟩

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