The Kaṭapayādi system of numerical notation and its spread outside Kerala

Rajeswara Sarma, Sreeramula

Revue d'histoire des mathématiques, Tome 18 (2012) no. 1, pp. 37-66.

Alors que l’étude de la transmission des idées scientifiques entre l’Inde et le reste du monde a sa propre importance, il est également nécessaire d’examiner la transmission de celles-ci à l’intérieur du pays, entre les régions, de la langue sanskrite vers les langues régionales et vice-versa. Cet article se propose de cartographier la diffusion du système Kaṭapayādi de notation numérique, largement répandu au Kérala, aux others parties de l’Inde, et montre que ce très important outil de notation mathématique, alors que bien connu en Inde du Nord, y a été rarement employé. D’autre part, cet article refute l’affirmation de Bibhutibhusan Datta et d’Avadhesh Narayan Singh sur l’existence de quatre variantes distinctes du système Kaṭapayādi et montre qu’en réalité il n’y en avait que deux, l’une d’entre elles étant limitée à un seul texte, d’origine inconnue.

While the study of the transmission of scientific ideas from and to India has its own importance, it is also necessary to examine the transmission of ideas within India, from one region to another, from Sanskrit to regional languages and vice versa. This paper attempts to map the spread of the Kaṭapayādi system of numerical notation, widely popular in Kerala, to other parts of India, and shows that this very useful tool of mathematical notation, though well known in northern India, was rarely employed there. The paper further refutes the contention of Bibhutibhusan Datta and Avadhesh Narayan Singh that there existed four distinct variants of the Kaṭapayādi system and shows that there were only two genuine variants of the system, one of these being limited to just one single text of unknown provenance.

Mots clés : Akṣarasaṃkhyā, Bhālūmal, Bhāskara II, Bhūtasaṃkhyā, Harṣa, inscriptions, Kaṭapayādi system, magic squares, Rāmacandra Vājapeyin, Sanskrit astrolabes, Sanskrit celestial globes

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