Mathematics and Astronomy.
The only work dealing with this subject as a whole is Thibaut’s Astronomie, Astrologie und Mathematik, in Bühler-Kielhorn’s Encyclopædia, 1899 (full bibliography). See also Cantor, Geschichte der Mathematik, pp. 505–562, Leipsic, 1880. Mathematics are dealt with in special chapters of the works of the early Indian astronomers. In algebra they attained an eminence far exceeding anything ever achieved by the Greeks. The earliest works of scientific Indian astronomy (after about 300 A.D.) were four treatises called Siddhāntas; only one, the Sūryasiddhānta (ed. and trans. by Whitney, Journ. Am. Or. Soc., vol. vi.), has survived. The doctrines of such early works were reduced to a more concise and practical form by Āryabhaṭa, born, as he tells us himself, at Pāṭaliputra in 476 A.D. He maintained the rotation of the earth round its axis (a doctrine not unknown to the Greeks), and explained the cause of eclipses of the sun and moon. Mathematics are treated in the third section of his work, the Āryabhaṭiya (ed. with comm. by Kern, Leyden, 1874; math. section trans. by Rodet, Journal Asiatique, 1879). Varāha Mihira, born near Ujjain, began his calculations about 505 A.D., and, according to one of his commentators, died in 587 A.D. He composed four works, written for the most part in the Āryā metre; three are astrological: the Bṛihat-saṃhitā (ed. Kern, Bibl. Ind., 1864, 1865, trans. in Journ. As. Soc., vol. iv.; new ed. with comm. of Bhaṭṭotpala by S. Dvivedī, Benares, 1895–97), the Bṛihaj-jātaka (or Horā-çāstra, trans. by C. Jyer, Madras, 1885), and the Laghu-jātaka (partly trans. by Weber, Ind. Stud., vol. ii., and by Jacobi, 1872). His Pancha-siddhāntikā (ed. and for the most part trans. by Thibaut and S. Dvivedī, Benares, 1889), based on five siddhāntas, is a karaṇa or practical astronomical treatise. Another distinguished astronomer was Brahmagupta, who, born in 598 A.D., wrote, besides a karaṇa, his Brāhma Sphuṭa-siddhānta when thirty years old (chaps. xii. and xviii. are mathematical). The last eminent Indian astronomer was Bhāskarāchārya, born in 1114 A.D. His Siddhānta-çiromaṇi has enjoyed more authority in India than any other astronomical work except the Sūrya-siddhānta.