Monday, March 27, 2023

Bhaskara’s ‘Lilavati’ : Gem of Mathematics

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Ancient Indian Mathematics is a branch of mathematics that has its roots in India and dates back to around the 3rd century BCE. This type of mathematics is known for its contributions to the development of mathematical concepts and techniques, such as the place value system and the use of zero. Ancient Indian mathematicians also made important contributions to geometry, trigonometry, and algebra.

Genius of Bhaskara

One of the most famous and influential ancient Indian mathematicians was Bhaskara, who lived in the 12th century. Bhaskara was born in a small village in western India and is believed to have been a Brahmin priest. He was a prolific writer and is known for his works on mathematics, astronomy, and astrology.

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Bhaskara is best known for his book Lilavati, which was written in 1150 CE. The book is considered to be one of the greatest works of ancient Indian mathematics and is still widely studied and admired today.

Lilavati the book

Bhaskara’s Lilavati is a collection of mathematical problems and solutions, presented in the form of a dialogue between Bhaskara and his daughter, Lilavati. The book covers a wide range of mathematical topics, including arithmetic, algebra, geometry, trigonometry, and astronomy.

One of the most interesting features of Lilavati is its use of word problems to illustrate mathematical concepts.

For example, Bhaskara might describe a scenario in which a man wants to measure the height of a building and uses mathematics to determine the solution.

This approach makes the mathematical concepts more relatable and helps to deepen the reader’s understanding of the material.


Another notable aspect of Lilavati is Bhaskara’s use of the decimal system. He was one of the first mathematicians to use decimal notation for representing numbers and to understand the concept of place value. This allowed him to perform complex calculations much more efficiently than was possible with the earlier numerical systems that were used in ancient India. This also made it easier for people to perform mathematical calculations as they did not have to rely on a memorization of the values of each numeral.

Bhaskara’s contributions to Trigonometry

Bhaskara also made significant contributions to the field of trigonometry. In Lilavati, he derived many of the basic trigonometric functions and formulas that are still used today. He was also the first mathematician to use the sine and cosine functions to calculate the values of angles and distances in a triangle. This was a major breakthrough in the field of mathematics and had a profound impact on the development of trigonometry.

In addition to his contributions to mathematics, Bhaskara was also a skilled astronomer and made many important observations about the movements of the planets and stars. He used his mathematical skills to develop methods for predicting eclipses and other astronomical events. His work on astronomy had a significant impact on the development of this field and is still studied and respected today.


Lilavati has been translated into many languages and continues to be a popular mathematical textbook even today. It is widely used in India and other parts of the world as a reference for students of mathematics. The book is not only a valuable resource for learning about ancient Indian mathematics, but it is also a testament to Bhaskara’s legacy as one of the greatest mathematicians of ancient India.

In conclusion, Ancient Indian Mathematics, and Bhaskara’s book Lilavati in particular, are important milestones in the history of mathematics. These contributions demonstrate the depth and breadth of mathematical knowledge in ancient India.




  • “Ancient Indian Mathematics” by The MacTutor History of Mathematics Archive (
  • “Bhaskara” by The Mathematics Genealogy Project (
  • “Lilavati: An Ancient Indian Mathematical Textbook” by MathPages (
  • “Bhaskara: An Indian Mathematician and Astronomer of the 12th Century” by S. R. Srinivasa Varadhan in “Indian Journal of History of Science” (Vol. 10, No. 1, 1975)
  • “The Mathematical Sciences in Ancient India” by A. K. Bag in “Current Science” (Vol. 87, No. 11, 2004)
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