Bhaskaracharya-II (1114 – 1193 CE)

.Undoubtedly, the greatest name in the history of ancient and medieval Indian astronomy and mathematics is that of Bhaskaracharya-II. His mathematical work Lilavati is the most popular book of traditional Indian mathematics. Some historians opine that Bhaskaracharya was from Karnataka while some view that he hails from Nashik district of Maharashtra.

Bhaskaracharya’s works

Bhaskara II composed a number of works (all in Sanskrit), three of which are very famous:

* Lilavati (on arithmetic, geometry, mensuration, etc.) which is the most popular work on ancient Indian mathematics.

* Bijaganita (on algebra including indeterminate analysis) which is a standard Hindu work on algebra.

* Siddhanta Siromani which is a standard work on Hindu astronomy, and is supplied with author’s own commentary calledVaasana Bhaashya.

Usually it is customary to regard Lilavati, Bijaganita, Grahaganitaand Goladhyaya as the four parts of the Siddhanta Siromani to make it a comprehensive treatise of Bhaskaracharya’s Hindu mathematical sciences. It is noteworthy that he had composed this great work in 1150 AD, i.e. when he was just 36 years old!

Two among his other works are the Karnakutuhala (whose epoch is 1183 AD) and a commentary on Lallacharya’sShisyadhivriddhida tantra (768 AD).

Lilavati (The Beautiful)

It belongs to the class of works called Patiganita, i.e. elementary mathematics covering arithmetic, algebra, geometry and mensuration. Its popularity is shown by the fact that it is still used as a text book in the Sanskrit-medium institutions throughout India. It provides the basic mathematics necessary for the study of almost all practical problems, including astronomy. The subject matter is presented through rules and examples in the form of about 270 verses which can be easily remembered. 

The great popularity of Lilavati is illustrated by the large number of commentaries written on it since it was composed. Many commentaries were written in Sanskrit by mathematicians of different periods, commentaries were written in regional languages and a few modern scholars like H.T.Colebrooke (London, 1817 CE), have given the English translation on original sanskrit text and commentaries.


It served as a text book for Sanskrit medium courses in higher mathematics. In it, the author included an exposition based on the earlier works. Among the sources named were the algebraic works of Sridhara and Padmanabha. There is a separate chapter on the Indian cyclic method called Cakravala. He attributes the methods to earlier teachers but does not specify any name. Due to the difficult nature of some of the topics,Bijaganita was not as popular as the Lilavati.

Siddhanta Siromani

It has two sections – Grahaganita (Planetary Mathematics) and the Goladhyaya (Spherics). Often these two sections appear as independent works. There is a lucid commentary on the whole work by the author himself. It is called Mitakshara orVasanabhasya. The 14th chapter of Goladhyaya is the is theJyotpatti, which may be regarded as a small tract on Hindu trigonometry.

Bhaskara is also credited as the pioneer of the principles of differential calculus. He explained Differentiation and Integration long before Newton & Leibnitz.

His professional expertise and all-round knowledge made him truly great and revered Acharya of Hindu astronomy and mathematics for generations.~ References1. The History of Mathematics and Mathematicians of India, by Er. Venugopal D. Heroor.

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