26 March 2021

**Q) Indian mathematicians have played a pivotal role in development of the field of mathematics in the world. Elucidate with suitable examples. (150 Words)**

Source: The IE Editorial: An act of diminution

GS 1: Indian Culture will cover the salient aspects of Art Forms, literature & Architecture from ancient to modern times.

**Approach Answer:**

**Introduction: **Indian literature is source of great amount of mathematics since the ancient times. The mathematical activity spurred in the Golden period of India (c. 4th to 6th century AD). This is marked by the birth of classical period of Indian mathematics (400-1600AD).

**The Contribution to Mathematics from India: **

**1. Decimal Number system**: The Yajurveda (1200-900 BCE) notes ways to write down numbers in decimal system upto a trillion.

**2. Geometrical ratios**: Baudhayana (c. 8th century BCE) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as: (3, 4, 5), (5,12,13). He also established a way to compute square root of two, which is the length of a diagonal of a unit square. Similar themes were touched upon by Katyayana in his works in c. 3th century BCE.

**3. Early Logic**: Indian Grammarians such as Panini(500 BCE) and Gotama gave rules of grammar to form **logical propositions.**

**4. Trigonometry**: Although the author of Surya Siddhanta (c. 4th century AD) is unknown. But the work is celebrated as the origin of Trigonometry. It defines trigonometric functions Sine(Jya) and Cocine(Kojya). Similarly the earliest uses of Tangent, Inverse sine etc. are found in it. This was contributed by Aryahatta and Varahminira who gave Trigonometric formulas.

**5. Computation of ****π: **Aryabhatt, the most celebrated Indian mathematician counted the value of π up to four places of decimal as 3. 1416 which was most accurate computation up to 1200 years later.

**6. Early Algebra**: Algebric Equations were used in India in c. 4th century AD. Aryabhatta is known to use quadratic equations, which was improve upon by Bhaskara I.

**7. Geometry**: Brahmagupta worked on cyclic quadrilateral. Aryabhatta introduced spherical Trigonometry and computing the Trigonometric ratios. He also developed solid geometry which as later on improved by Bhaskara II.

**8. Zero**: It is said that the Buddhist idea of Shunyavada(voidness) (c. 1st century AD) gave rise to the mathematical idea of Shuya(Zero). Later Brahmagupta in gave first systematic formulations of rules of zero.

**9. Negative number****s**: Brahmagupta also introduced rules for negative numbers. Later Kannada Jain Mathematician Mahavira(c. 9th Century) negative number algebra.

**10. Mathematics for commerce**: Although these ideas have been used in commerce for long. But it was Bhaskara II(11th Cent) who gave rules for computations of interests.

**11. Geometrical Series**: The mathematicians from Kerala established their expertise in the formulation of geometric series, which helped in computation of π and other irrational numbers such as ratios of sine and square roots.

**12. Astronomy**: The mathematics is closely linked to Astronomy. Those who have understanding of Solid geometry can easily refute Geocentric model of the world. Contrary to popular belief many mathematicians like Aryabhatta and Kerala School led by Bhaskarachayra II could easily conclude the spherical shape of earth and motions of planets.

**Conclusion: **The Mathematicians around the world have been charged with Euro-centrism, which ignores Indian contributions to mathematics. However, the forgetfulness also lies in the fact that the mathematical ideas in India were propagated only in a closed community, which eventually stagnated in 1700s. Only in 20th century, it was the genius of Ramanuja who gathered the pieces of mathematics to amaze the world with Indian imagination in the field of number system and Trigonometry.

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