Indian Mathematics - A Short Note

In ancient India, mathematics or 'Ganita' was the 'Science of Calculations'. It was primarily studied in the context of numerical computation and geometric measurement. Most of the Indian mathematical work can be found as a part of 'Jyotisha' or Astronomy. This is because Astronomy, which dealt with the measurement of time using the heavenly bodies, involved high levels of sophisticated numerical computation. Mathematics in ancient India was so well developed that the body of knowledge was not restricted only to the elite scholars. It was prevalently used even by the common people in their daily activities and profession.

The history of Indian mathematics dates back to the vedic period (around 1500 B.C.) The 'Sulbasutras' of this vedic age are texts on rules for altar construction. They are the oldest texts on Indian mathematics. They contain the general enunciation of the Pythagoras theorem,  approximate value for square root of 2, methods of transforming one figure to another etc... Indians also used the decimal place-value system of representing the numbers. They had a representation for zero. The origin of the decimal place-value system in India was sometime around 1st century B.C.

There are numerous great mathematicians who have contributed to Indian Mathematics. The subject is a synergistic effort of all of them. Since even a mention of all of them would run into pages, we are able to list the contributions of only a few of the mathematicians. The set that we have described below is only a drop in the ocean of great mathematicians who lived in India.


Aryabhatta was a 5th century mathematician and astronomer who worked  in the following areas- the methods of determining square and cube roots, geometrical problems, the progression, problems involving quadratic equations and indeterminate equations of the first degree. The method of solving these equations has been called Kuttaka by later mathematicians. He was the first astronomer to mention that the diurnal motion of the heavens is due to the rotation of the earth about its axis. Other contributions Aryabhatta made towards pure mathematics were his sine tables, his approximation of pi and the expressions that he gave for the sum of squares and the sum of cubes. All his work is documented in the Aryabhatiya.


Brahmagupta was a 6th century mathematician and astronomer. He is believed to be the inventor of the concept of zero. He designed a method for solving equations of the type Nx2 + 1 = My2. These type of equations are known as 'Varga Prakriti'. He also gave rules to solve simple quadratic equations. The first to use algebra in astronomy, all his work is documented in the 'Brahma Sputa Siddhanta'. It was through this work that the Arabs first heard of astronomy. His contributions to astronomy include calculations for the motions of various planets, the rising and setting of the sun and the moon and, solar and lunar eclipses. Brahmagupta was one of the very few early Indian mathematicians, who conceptualised the earth as round, and not as flat and hollow.


Bhaskara was a 12th century mathematician and astronomer. He was the head of the Ujjain observatory. His work was mainly in algebra. He was influenced by Aryabhatta's work on Kuttaka and made his own modifications in order to solve indeterminate equations of the second degree. (example : Nx2 + 1 = My2 ).  This is known as the chakravala process. Bhaskara wrote the 'Siddhanta Siromani', which has 4 parts to it - Lilavati (arithmetic), Bijaganita (algebra), Grahaganita (maths of the planets) and Goladhyaya (chapter on the celestial globe). In the Bijaganita, a rough explanation of the concept of infinity occurs, in terms of the fact that any number divided by 0, gives infinity.

He had clear ideas of differential calculus. In the Goladhyaya, he gave the value of the ratio of the circumference of a circle to its diameter. The picture shown above, is claimed to be from the Bijaganita.

There are a lot of other mathematicians who have contributed to the world of Indian mathematics. Now, go on and do some research to find out about some of them.    

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