# Contribution of Indian Mathematicians

# Famous Indian Mathematicians and their Contributions

History of mathematics will remain indebted forever to the contribution of Indian mathematicians. In this post I will like to draw your attention towards the contribution of some famous Indian mathematicians dating from the Vedic period to the modern times. They have contributed significantly. However, many of them did not get their due recognition due to insufficient follow up by the later generations.

## Baudhayana

It was Baudhayana who discovered the Pythagoras Theorem 1000 years before Pythagoras was born! He stated that a rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together. This is such an incredible way of visualizing Pythagoras theorem.

## Aryabhatta

He is probably the most celebrated Indian mathematician. He approximated the value of pi correctly upto five decimal places and discussed the concept of sine.

He gave the area of a triangle as the result of perpendicular multiplied by half-side.

In algebra, Aryabhatta summed series of squares and cubes and also solved indeterminate equations of the type ax -by = c.

He was the first one to calculate the time period of earth’s rotation as 365 days!

## Brahmagupta

He is the one who gave us the concept of zero and negative numbers.

He proposed rules for the solution of quadratic and simultaneous equations and calculated area of a cyclic quadrilateral with ‘s’ as semiperimeter.

Founder of the branch of higher mathematics known as “Numerical Analysis”, he gave the solution of the indeterminate equation Nx²+1 = y².

The identity x²- y² = (x+y)(x-y) is attributed to him.

## Bhaskara

He expanded the work of Aryabhatta and found a rational approximation of the sine function.

First to write Hindu-Arabic numerals and zero(as ‘0’), he declared that any number divided by zero is infinity and that the sum of any number and infinity is also infinity!!

Bhaskara introduced chakrawal, or the cyclic method, to solve algebraic equations. Six centuries later, European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it “inverse cyclic”.

Bhaskara laid the foundation of differential calculus. He gave an example of what is now called “differential coefficient” and the basic idea of what is now called “Rolle’s theorem”. Unfortunately, later Indian mathematicians did not take any notice of this. Five centuries later, Newton and Leibniz developed this subject.

## Mahavira

A Jain mathematician, Mahavira gave the derivation of the volume of a frustum by a sort of infinite procedure.He worked with the concept of ardhaccheda: the number of times a number could be divided by 2; effectively logarithms to base 2.He also worked with logarithms in base 3 and base 4.

## Varahamihira

His mathematical contributions include the discovery of trigonometric formulas:

## Bhaskara II

He was a mathematician-astronomer who gave a proof for division by zero being infinity. He declared that a positive number has two square roots and also discovered the derivative and the differential coefficient.

## Srinivasa Aaiyangar Ramanujan

In modern India, Ramanujan has gained substantial fame as a mathematician. Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan’s identities in partition of numbers, work on algebra of inequalities, elliptic functions, continued fractions, partial sums and products of hypergeometric series are his main contribution.

1729 is popularly called Ramanujan Number. Click to know more about Ramanujan Number

## P.C. Mahalanobis

He founded the Indian Statistical Research Institute in Calcutta. In 1958, he started the National Sample Surveys which gained international fame.

## C.R. Rao

A well known statistician, famous for his “theory of estimation”(1945). His formulae and theory include ‘Cramer -Rao inequality’, ‘Fischer -Rao theorem’ and ‘Rao – Blackwellisation’.

## D.R. Kaprekar

Dattaray Ramachandra Kaprekar, was a school teacher in Devlali near Nashik, Maharashtra. He never received a masters degree and was laughed at by his contemporary mathematicians for his work being too trivial and unimportant. But today he is hailed as a great recreational mathematicians of India. Fond of numbers, Kaprekar is well known for “Kaprekar Constant” 6174. Take any four digit number in which all digits are not alike. Arrange its digits in descending order and subtract from it the number formed by arranging the digits in ascending order. If this process is repeated with reminders, ultimately number 6174 is obtained, which then generates itself. Apart from that he discovered Kaprekar Numbers, Harshad Numbers, Self-Numbers and much more.

## Harish Chandra

He greatly developed the branch of higher mathematics known as the infinite dimensional group representation theory.

## Narendra Karmarkar

He, working at Bell Labs USA, stunned the world in 1984 with his new algorithm to solve linear programming problems. This made the complex calculations much faster, and had immediate applications in airports, warehouses, communication networks etc.

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Great info !! To know more about other work by Indian mathematician read

Ganiti by achut Godbole (excellent marathi book)

Who had contributed in mid point theorum