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Āryabhaṭa I

(b. A. D.476).

Āryabhaṭa I clearly states his connection with Kusumapura (Pāṭaliputra, modern Patna in Bihar), which had been the imperial capital of the Guptas for much of the fourth and fifth centuries. The assertion of Nīlakaṇṭha Somasutvan (b. 1443) that Āryabhaṭa was born in the Aśmakajanapada (this presumably refers to the Nizamabad district of Andhra Pradesh) is probably the result of a confusion with his predecessor. Bhāskara I, as commentator on the Āryabhaṭīya, Āryabhaṭa I wrote two works: the Āryabhaṭīya in 499 (see Essay V), and another, lost treatise in which he expounded the ārddharātrika system (see Essay VI).

The Āryabhaṭīya consists of three parts and a brief introduction: Daśagītikā, introduction with parameters (ten verses); Gaṇitapāda, mathematics (thirtythree verses); Kālakriyāpāda, the reckoning of time and the planetary models (twenty-five verses); Golapāda, on the sphere, including eclipses (fifty verses). It was translated into Arabic in about 800 under the title Zīj al-Arjabhar, and it is to this translation that all the quotations in al-Bīrūnī refer, including those that led Kaye to conclude—mistakenly—that the Gaṇitapāda was not written by Āryabhaṭa I.

The Āryabhaṭīya has been commented on many times, especially by scholars of south India, where it was particularly studied. The names of those commentators who are known are as follows:

  1. Prabhākara (ca. 525). His commentary is lost.
  2. Bhāskara I (629). His Bhāsya is being edited by K. S. Śukla of Lucknow.
  3. Someśvara (fl. 1040). His Vāsanābhāsya is preserved in two manuscripts in the Bombay University Library.
  4. Sūryadeva Yajvan of Kerala (b. 1191). There are many manuscripts of his Bhaṭaprakāśa, in south India.
  5. Parameśvara(fl. 1400–1450). His Bhaṭadīpikā, based on Sūryadeva’s Bhaṭaprakāśa, was published by H. Kern (see below).
  6. Nīlakaṇṭha Somasutvan (b. 1443). His Bhāsya is published in Trivandrum Sanskrit Series (see below).
  7. Yallaya (fl. 1482). His Vyākhyāna is based on Sūryadeva’s Bhaṭaprakāśa; there is one manuscript of it in Madras and another among the Mackenzie manuscripts in the India Office Library.
  8. Raghunātha (fl. 1590). His Vyākhyāna is dealt with by K. Madhava Krishna Sarma, “The Āryabhaṭīyavyākhyā of Raghunātharāja—A Rare and Hitherto Unknown Work,” in Brahmavidyā, 6 (1942), 217–227.
  9. Kodaṇḍarāma of the Koṭikalapūḍikula, a resident of Bobbili in the Godāvarī district of Andhra Pradesh (fl. 1854). Besides an Āryabhaṭatantragaṇita, he wrote a Telugu commentary on the Āryabhaṭīya entitled Sudhātaran̄ga; it was edited by V. Lakshmi Narayana Sastri, in Madras Government Oriental Series, 139 (Madras, 1956).
  10. Bhūtiviṣṇu. There is apparently only one manuscript (in Berlin) and its apograph (in Washington, D. C.) of his commentary (Bhāsya) on the Daśagītikā.
  11. Ghaṭāgopa. There are two manuscripts of his Vyākhyā in Trivandrum.
  12. Virūpākṣa Sūri. There is a manuscript of his Telugu commentary in Mysore.

There also exists a Marāṭhī translation of the Āryabhaṭīya in a manuscript at Bombay.

There are several editions of the Āryabhaṭīya That by H. Kern (Leiden, 1874) is accompanied by the commentary of Parameśvara. Kern’s text and commentary were reprinted and translated into Hindi by Udaya Nārāyana Singh (Madhurapur, Etawah, 1906). A new edition of the text, with the commentary of Nīlakaṇṭha Somasutvan (who does not include the Daśagītikā), was published in three volumes: Vols. I and II by K. Sāmbśiva Śāstrī and Vol, III by Suranad Kunjan Pillai, in Trivandrum Sanskrit Series, 101, 110, and 185 (Trivandrum, 1930, 1931, 1957). The text has also been published accompanied by two new commentaries, one in Sanskrit and one in Hindi, by Baladeva Mishra (Patna, 1966). The Gaṇitapāda was translated into French by Léon Rodet, in Journal Asiatique, 7, no. 13 (1879), 393–434; and into English by G. R. Kaye, in Journal of the Asiatic Society of Bengal, 4 (1908), 111– 141 . Complete English translations have been made by Baidyanath Rath Sastri (Chicago, 1925; unpub.); P. C. Sengupta, Journal of the Department of Letters of Calcutta University, 16 (1927), 1–56; and W. E. Clark (Chicago, 1930).


It is intended here to include references only to those books and articles that are primarily concerned with Āryabhata I and his works; the many other papers and volumes that mention and/or discuss him can be found listed in David Pingree Census of the Exact Sciences in India. Listed chronologically, the references are F.-E. Hall, “On the Ārya-siddhānta,” in Journal of the American Oriental Society, 6 (1860), 556–559, with an “Additional Note on Āryabhaṭṭa and his Writings” by the Committee of Publication (essentially W. D. Whitney), ibid., 560–564; H. Kern, “On Some Fragments of Āryabhaṭa,” in Journal of the Royal Asiatic Society20 (1863), 371–387 repr. in Kern’s Vespreide Geschriften I (The Hague, 1913), 31–46; Bhāu Dājī, “Brief Notes on the Age and Authenticity of the Works Āryabhaṭa, Varāhamihira, Brahmagupta, Bhaṭṭotpala, and Bhāskarāchāya,” in Journal of the Royal Asiatic Society (1865), pp. 392–418 (Āyabhatya only pp. 392–406, 413–414); L. Rodet, “Sur la véritable signification de la notation numérique inventée par Āryabhaṭa” in Journal Asiatiqeu, ser. 7, 16 (1880), 440–485; Sudhākara Dvivedin Gaṇakatarn̄giṇī (Benares, 1933; repr. from The Pandit, 14 [1892]), 2–7; Ś. B. Dīkṣita, Bhāratīya Jyotiḥśāstra (Poona, 1931; repr. of Poona ed., 1896), pp. 190–210; G. Thibaut, Astronomie, Astrologie und Mathematik, Grundriss der indo-arischen Philologie und Altertumskunde, III, pt. 9, (Strasbourg, 1899), 54–55; T. R. Pillai, Ārybhaṭa or the Newton of Indian Astronomy (Madras, 1905—not seen—reviewed in Indian Thought [1907], pp. 213–216); G. R. Kaye, “Two Āryabhaṭas,” in Bibliotheca mathematica, 10 (1910), 289–292; J. F. Fleet, “Āryabhaṭa’s System of Expressing Numbers,” in Journal of the Royal Asiatic Society (1911), pp. 109–126; N. K. Mazumdar, “Āryyabhatta’s Rule in Relation to Indeterminate Equations of the First Degree,” in Bulletin of the Calcutta Mathematical Society, 3 (1911/1912), 11–19; J. F. Fleet, “Tables for Finding the Mean Place of Saturn,” in Journal of the Royal Asiatic Society (1915), pp. 741–756; P. C. Sengupta, “Āryabhaṭa’s Method of Determining the Mean Motions of Planets,” in Bulletin of the Calcutta Mathematical Society, 12 (1920/1921), 183–188.

See also R. Sewell, “The First Arya Siddhanta,” in Epigraphia Indica, 16 (1921/1922), 100–144, and 17 (1923–1924), 17–104; A. A. Krishnaswami Ayyangar, “The Mathematics of Āryabhaṭa,” in Quarterly Journal of the Mythic Society, 16 (1926), 158–179; B . Datta, “Two Āryamaṭas of al-Biruni,” in Bulletin of the Calcutta Mathematical Society, 17 (1926), 59–74; S. K. Ganguly, “Was Āryabhaṭa Indebted to the Greeks for His Alphabetical System of Expressing Numbers?,” ibid., 195–202, and “Notes on Ārayabhaṭa,” in Journal of the Bihar and Orissa Research Society12 (1926), 78–91; B. Datta, “Āryabhaṭa, the Author of the Gaṇita,” in Bulletin of the Calcutta Mathematical Society, 18 (1927), 5–18; S. K. Ganguly, “The Elder Āryabhata and the Modern Arithmetical Notation,” in American Mathematical Monthly, 34 (1927) 409–415; P. C. Sengupta, “Āryabhaṭa, the Father of Indian Epicyclic Astronomy,” in Journal of the Department of Letters of Calcutta University, 18 (1929), 1–56; S. K. Ganguly, “The Elder Āryabhaṭa’s Value of π,” in American Mathematical Monthly, 37 (1930), 16–29; P. C. Sengupta, “Āryabhata’s Lost Work,” in Bulletin of the Calcutta Mathematical Society22 (1930), 115–120; B . Datta, “Elder Āryabhaṭa’s Rule for the Solution of Indeterminate Equations of the First Degree,” ibid., 24 (1932), 19–36; P. K. Gode, “Appayadīkṣita’s Criticism of Āyabhaṭa’s Theory of the Diurnal Motion of the Earth (Bhūbhramavāda),” in Annals of the Bhandarkar Oriental Research Institute, 19 (1938), 93–95, repr. in Gode’s Studies in Indian Literary History, II, Singhi Jain Series, 38 (Bombay, 1954), 49–52; S. N. Sen, “Āryabhaṭa’s Mathematics,” in Bulletin of the National Institute of Sciences of India, 21 (1963), 297–319; Satya Prakash, Founders of Sciences in Ancient India (New Delhi, 1965), pp. 419–449.

David Pingree