“Āryabhaṭa’s Saṅkhyāvinyāsa”, Brhat, June 12, 2026
“Āryabhaṭa devised a unique saṅkhyāvinyāsa[1] (numeration system) that uses the saṃskṛtavarṇamālā, i.e., the svaras (vowels) and vyañjanas (consonants). He presents this in his work Āryabhaṭīya (6th century CE). The saṅkhyāvinyāsa employs vyañjanas as numeric digits and vowels as positional markers, allowing very large numbers to be expressed within poetic verse. Āryabhaṭa devised this saṅkhyāvinyāsa as large numbers were part of regular calculations in Siddhāntajyotiṣa, the branch of traditional vaidika astronomy focused on astronomical calculations, planetary positions, and mathematical modeling of the cosmos. Siddhāntajyotiṣa also covers the mechanics of time, eclipses, and orbital positions and is often inseparable from Gaṇitaśāstra (mathematics).
The second verse in the Gītikāpāda of Āryabhaṭa’s Āryabhaṭīya is as follows –
वर्गाक्षराणि वर्गेऽवर्गेऽवर्गाक्षराणि कात् ङ्मौ यः। खद्विनवके स्वरा नव वर्गेऽवर्गे नवान्त्यवर्गे वा॥१-२॥
vargākṣarāṇi varge’varge’vargākṣarāṇi kāt ṅmau yaḥ| khadvinavake svarā nava varge’varge navāntyavarge vā||1-2||
“The varga letters in the varga (places) and the avarga letters in the avarga (places). From k onwards, y is equal to ṅ plus m. In the places of the two nines of zeros, the nine vowels should be written. In the varga places beyond the nine vowels too…….”
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