Bhaskara II

Bhāskara II

Bhāskara(ಭಾಸ್ಕರ ೨) (also known as Bhāskarāchārya ("Bhāskara the teacher"), and as Bhāskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer. He was born in Bijapur in Karnataka.

Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work Siddhānta Shiromani, (Sanskrit for "Crown of Treatises") is divided into four parts called Lilāvatī, Bījagaṇita, Grahagaṇita and Golādhyāya, which are also sometimes considered four independent works. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇa Kautūhala.

Bhāskara's work on calculus predates Newton and Leibniz by over half a millennium. He is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhāskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.

Bhāskara gives his date of birth, and date of composition of his major work, in a verse in the Āryā metre:

rasa-guṇa-pūrṇa-mahīsama
śhaka-nṛpa samaye 'bhavat mamotpattiḥ /
rasa-guṇa-varṣeṇa mayā
siddhānta-śiromaṇī racitaḥ //

This reveals that he was born in 1036 of the Śhaka era (1114 CE), and that he composed the Siddhānta Śiromaṇī when he was 36 years old. He also wrote another work called the Karaṇa-kutūhala when he was 69 (in 1183). His works show the influence of Brahmagupta, Sridhara, Mahāvīra, Padmanābha and other predecessors.

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