Bhāskara-prabhā

He is known as Bhāskara, Bhāskarācārya (“Bhāskara the teacher”), and Bhāskara II (to distinguish him from an earlier mathematician of the same name). Born in 1114, he was one of the greatest mathematicians of India, known for his mathematics, his astronomical texts, and also his poetical and literary style. Perhaps his most famous book is the Līlāvatī, which ranges from elementary arithmetic to algebra, but he also produced a second book on mathematics and two important books on astronomy, including the massive Siddhāntaśiromaṇi. Bhāskara wrote in elegant verse, but he also produced an “auto-commentary” in prose, tersely explaining his own verse.

This book is the result of a conference celebrating the 900th anniversary of Bhāskara’s birth, held in 2014 at the Vidya Prasarak Mandal in Thane, India. It is a collection of mostly technical articles on Bhāskara’s life and work. The articles are organized into seven sections. The middle five sections contain studies of Bhāskara’s four main texts, with the Siddhāntaśiromaṇi getting two sections. The first section contains more general articles about Bhāskara’s life and work, and the final section includes a couple of articles on the reception his works.

The editors provide an introduction that serves both as an excellent introductory account of Bhāskara’s life and work and as a summary of the individual articles. Students looking for something more substantial than Wikipedia or MacTutor will find good information here, including some corrections to internet “truth.” Also interesting is an article by S. R. Sarma on “The Legend of Līlāvatī,” in which he refutes the well-known story linking the book’s title to Bhāskara’s daughter. Sarma also offers conjectures what the source of this legend might have been and some examples of modern variations and elaborations. This too is a useful correction to common “knowledge.”

Many articles clearly assume a knowledgeable reader. For example, K. Ramakalyani contributes an interesting article on a 16th-century commentary on the Līlāvatī. It is called “Gaṇeśa Daivajn̄a’s upapattis for some rules in the Līlāvatī.” Nowhere in the article can one find a translation of ”upapatti“ (Sarma, in his article, glosses it as “rationale”). This is fairly typical: Sanskrit terms are often used without explanation. Longer texts are usually given in the original, then a transcription, and then a translation. A particularly welcome example of this is a 1207 inscription about Bhāskara’s life and work, which is presented in full.

Students of the mathematics of India will, of course, find much here that is useful, and at least some of the articles will interest more general readers as well.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College.