24 2. MATHEMATICAL CULTURES Ithe Sun), from the late fourth century, has survived intact. Another from approx-
imately the same time, the Paulisha Siddhanta, was frequently referred to by the
Muslim scholar al-Biruni (973-1048). The name of this treatise seems to have been
bestowed by al-Biruni, who says that the treatise was written by an Alexandrian
astrologer named Paul.2.5. Aryabhata I. With the writing of treatises on mathematics and astronomy,
we at last come to some records of the motives that led people to create Hindu
mathematics, or at least to write expositions of it. A mathematician named Aryab-
hata, the first of two mathematicians bearing that name, lived in the late fifth
and early sixth centuries at Kusumapura (now Pataliputra, a village near the city
of Patna) and wrote a book called the Aryabhatiya. This work had been lost for
centuries when it was recovered by the Indian scholar Bhau Daji (1822-1874) in- Scholars had known of its existence through the writings of commentators
and had been looking for it. Writing in 1817, the English scholar Henry Thomas
Colebrooke (1765-1837), who translated other Sanskrit mathematical works into
English, reported, "A long and diligent research of various parts of India has, how-
ever, failed of recovering any part of the... Algebra and other works of Aryabhata."
Ten years after its discovery the Aryabhatiya was published at Leyden and attracted
the interest of European and American scholars. It consists of 123 stanzas of verse,
divided into four sections, of which the first, third, and fourth are concerned with
astronomy and the measurement of time.
Like all mathematicians, Aryabhata I was motivated by intellectual interest.
This interest, however, was closely connected with his Hindu piety. He begins the
Aryabhatiya with the following tribute to the Hindu deity.
Having paid reverence to Brahman, who is one but many, the true
deity, the Supreme Spirit, Aryabhata sets forth three things: math-
ematics, the reckoning of time, and the sphere. [Clark, 1930, p. 1]The translator adds phrases to explain that Brahman is one as the sole creator of
the universe, but is many via a multitude of manifestations.
Aryabhata then continues his introduction with a list of the astronomical ob-
servations that he will be accounting for and concludes with a promise of the reward
awaiting the one who learns what he has to teach:
Whoever knows this Dasagitika Sutra which describes the move-
ments of the Earth and the planets in the sphere of the asterisms
passes through the paths of the planets and asterisms and goes to
the higher Brahman. [Clark, 1930, p. 20]As one can see, students in Aryabhata's culture had an extra reason to study
mathematics and astronomy, beyond the concerns of practical life and the pleasures
of intellectual edification. Learning mathematics and astronomy helped to advance
the soul through the cycle of births and rebirths that Hindus believed in.
After setting out his teaching on the three subjects, Aryabhata concludes with
a final word of praise for the Hindu deity and invokes divine endorsement of his
labors: