The Two Bhaskaras

Summary

This article distinguishes between two important Indian mathematicians who are often conflated: Bhāskara I of the seventh century and Bhāskara II (Bhāskarācārya) of the twelfth century. The author begins by outlining the historical context and major works of each scholar. Bhāskara I wrote commentaries on the Āryabhaṭīya and is credited with an early sine table and a formula for approximating the sine function. Bhāskara II, on the other hand, authored the Siddhāntaśiromaṇi, which consists of four sections dealing with arithmetic, algebra, planetary motion and the sphere. A notable achievement of Bhāskara II is the Lilāvatī, a treatise on arithmetic presented through poetic problems. The article points out that later writers sometimes attributed results from the Siddhāntaśiromaṇi to the earlier Bhāskara. By analysing manuscript colophons and stylistic features, the author shows that the two mathematicians belonged to different linguistic regions and intellectual traditions. Bhāskara I’s language is simpler and more didactic, whereas Bhāskara II employs ornate verse and complex algebraic procedures. The paper also discusses the influence of each mathematician on subsequent astronomers, noting that Bhāskara I’s commentary preserved Āryabhaṭa’s methods, while Bhāskara II’s work was a standard text for centuries. In conclusion, the author urges historians to credit innovations accurately and to recognise the distinct contributions of the two Bhāskaras.