**Discuss the significant contributions made by Indians to the field of mathematics. (200 Words)**

**Baudhayana’s**

**Śulbasūtras****:**

- The Pythagoras theorem finds a place in Baudhayana’s
*Śulbasūtras*, which dates back to about 800 BC—more than 200 years before Pythagoras was born.

**Aryabhata:**

- The first comprehensive use of the place value system of arithmetic was found in
*Āryabha**ṭ**īya*(499CE), a famous work of Aryabhata. - The trigonometric function “sine” traces its origin to
*jya-ardha*series, a table of half-chords of a unit radius circle, compiled by him.

**Varahamihira:**

- He improved the accuracy of Aryabhata sine tables.
- He included the discovery of many trigonometric formulae
- Was among the first mathematicians to discover a version of what is now known as Pascal’s triangle

**Brahmagupta:**

- The most significant contribution of
__Brahmagupta__was the introduction of zero(0) to the mathematics which stood for “nothing”.

**Bhaskara I**

- Bhāskara was the one who declared that any number divided by zero is infinity and that the sum of any number and infinity is also infinity. He is also famous for his book “Siddhanta Siromani”.

**Bhaskara II:**

- Pell’s equation, attributed by 18th century Swiss mathematician Leonhard Euler to 17th century English mathematician John Pell was originally solved by Bhaskara II, a 12th century Indian mathematician-astronomer.

**Madhava:**

- Similarly, much of the work on calculus was done in India by the Kerala School of Mathematics—much before Isaac Newton and Gottfried Wilhelm Leibniz came into the picture—founded by Madhava in the 14th century CE

**Srinivasa Ramanujan**

**:**

- is one of the celebrated Indian mathematicians. His important contributions to the field include
__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.

**Calyampudi Radhakrishna Rao**, popularly known as C R Rao is a well known statistician, famous for his “theory of estimation”.

**D.R. Kaprekar (1905-1988) :**

- 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.

**Narendra Karmarkar :**

- India born Narendra Karmarkar, 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

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