Bhaskara II is a famous mathematician of ancient India. He was born in 1114
A.D. in the city of Bijapur, Karnataka state, India. Peoples also know him as Bhaskaracharya,
which means “Bhaskara the Teacher”. His father name was Mahesvara. By profession
he was an astrologer, who taught him mathematics, which he later passed on to his
son Loksamudra. In many ways, Bhaskaracharya represents the peak of mathematical
knowledge in the 12th century. He reached an understanding of the number systems
and solving equations, which was not to be achieved in Europe for several centuries.
Bhaskara II became head of the astronomical observatory at Ujjain, which
was the leading mathematical centre in India at that time. It also goes to the credit
of Varahamihira and Brahmagupta, the top mathematicians who worked there and built
up this school of mathematical astronomy. He wrote six books and but a seventh work,
which is claimed to be by him, is thought by many historian to be a late forgery.
The topics of his six books are geometry, trigonometry, calculus, algebra arithmetic
and astronomy. The six works are Lilavati (The Beautiful) on mathematics; Bijaganita
(Root Extraction) on algebra; the siddhanta shiromani which is divided into two
parts: mathematical astronomy and sphere; the Vasanabhasya of Mitaksara which is
Bhaskaracharya’s views on the Siddhantashiromani; the Karanakutuhala (Calculation
of Astronomical Wonders) or Brahmatulya in which he simplified the concepts of Siddhantashiromani;
and the Vivarana which comments on the Shishyadhividdhidatantra of Lalla. From the
mathematical point of view, the first three of these works are the most interesting.
Bhaskara II also wrote Siddhanta Shiromani at the age of 36 in 1150 A.D.
This colossal work has divided into four categories Goladhyaya, Ganitadhyaya, Lilavati
and Bijaganita and consists of about 1450 verses. Each and every categories of the
book consigns of huge number of verses. Each of them can be considered as a separate
book, Lilavati has 278 verses, Bijaganita has 213 verses, Ganitadhyaya has 451 verses,
and Goladhyaya has 501 verses. He formulated simple ways of calculations from Arithmetic
to Astronomy in this book. He wrote Lilavatis an excellent lucid and poetic language.
It has been translated in various languages throughout the world. In English, the
multiples of 1000 are termed as thousand, million, billion, trillion, quadrillion
etc. These terms were named recently in English, but Bhaskaracharya gave the terms
for Numbers in multiples of ten, which are as follows:
Eka (1), dasha (10), shata (100), sahastra (1000), ayuta (10000), laksha (100000),
prayuta (1,000,000 = million), koti (107), arbuda (108), abja (109=billion), kharva
(1010), nikharva (1011), mahapadma (1012=trillion), Shankh (1012), Jaladhi (1014),
antya (1015=quadrillion), Madhya (1016) and parardha (1017).
The Siddhanta siromani too enjoyed great popularity. Bhaskara II calculated the
equinoctial shadow at any place and the new corrections to be applied to the calculation
of the time of sunrise. Bhaskara too accepted the precession of the equinoxes, through
later astronomers allowed Bhaskara’s correct theory to be perverted. All this shows
beyond doubt that Bhaskara was blessed with a remarkably active brain. Bhaskara’s
works have served as reference books in every nook and corner of India. He died
in 1185 in Ujjain, India.