Indian Contribution To The World
16. Indian Contribution to the world
16.1. Mathematics
We do realize that the inventions and the discoveries we present are just the tip of the
iceberg because of a lack of documentation on the earlier periods and because the
material covered here is meant to be accessible to Middle School students and beyond.
We can divide the duration of interest into the following periods and recognize some well-known people belonging to those periods.
Vedic (1500 BC to 500 BC): E.g., Baudhayana, Panini, etc.
Classical (500 BC to 1100 AD): E.g., Aryabhata, Aryabhata II, Bhaskara, BhaskaraII, Brahmagupta, Varamihira, Shridhara, etc.
Medieval to Mughal Period (13th century to 1800): E.g., Nilakantha Somayaji,etc.
Born in 1800s: E.g., Srinivasa Ramanujan, Satyendra Nath Bose, ChandrasekharVenkat Raman, etc.
Born in 1900s: E.g., Subrahmanyan Chandrasekhar, Venkatraman Ramakrishnan,etc.The subject areas where we have had a lot of influence include:
Generative Grammars for defining languages.
Arithmetic with the invention of zero and the positional number system.
Vedic Mathematics that provides sound shortcuts to carry out arithmeticoperations.
Geometry such as by providing alternative proofs for the Pythogoras Theorem.
Number Theory, an abstract and difficult area of pursuit.
In what follows, we expand on specific contributions made by Indians to the fields of mathematics, science, and astronomy, and highlight its relevance to the current understanding where it is not obvious. We also provide some background on the motivations for the early developments.
16.2. Ancient Hindu Mathematicians and the Invention of Zero
Invention of zero and the positional number system is attributed to Indian
Mathematicians (500 AD) and is considered an extremely important step in the evolution of mathematics.
16.3. Driving Forces behind Early Mathematics
In Harrappan Period, the Decimal system was used in weights and measures for accuracy in trade and commerce.
In Vedic Period, the system of agricultural tax assessments required accurate measurement of cultivated areas. This meant that an understanding of geometry and arithmetic was essential for revenue administrators.
Arithmetic operations (Ganit) such as addition, subtraction, multiplication,
fractions, squares, cubes and roots are enumerated in the Narad Vishnu Purana attributed to Ved Vyas (pre-1000 BC). Baudhayana's Sutra displays an understanding of basic geometric shapes and techniques of converting one geometric shape (such as a rectangle) to another of equivalent (or multiple, or fractional) area (such as a square).
16.4. Vedic Mathematics
Vedas are texts from Ancient India in Sanskrit. Mathematics is the study of quantity (how much?), change (how fast?), space (shapes), etc. Vedic Mathematics has come to signify the mathematical knowledge of ancient Hindus passed down through generations (initially verbally and later codified) as slokas (verses) in Sanskrit.
Pythagoras (500 B.C.) is credited with the result that bears his name. The Pythagorean
Theorem states that, in a right angled triangle, the sum of the squares on the two
smaller sides (a,b) is equal to the square on the hypotenuse (c): a2 + b2 = c2 . A formal proof of this result appears in Euclid s (300 B.C.) Elements (Book 1 Proposition 47). However, it is also known that Baudhayana (800 B.C.) used it in Sulabh Sutras (appendix to Vedas) and Bhaskara (12th Century) gave alternate proofs. Baudhayana
(800 B.C.) gave an approximation to the valueof v2 and an approximate approach to finding
a circle whose area is the same as that of a square.Manava (700 B.C.) gave an
approximation to the value of ? as 3.125. a = 1 b = 2 c = v5
Modern Mathematicians
We now summarize some facts about a few recent famous Indian Mathematicians and Scientists, and their lasting contributions.
16.5. Srinivasa Ramanujan :
The Man who knew Infinity Born: 22 December 1887, Erode, Tamil Nadu, India. Died: 26 April 1920 (aged 32), Madras. Achievement: FRS Alma mater: Trinity College, Cambridge Academic advisors: G. H. Hardy and J. E. Littlewood He mastered Trignometry by S. L. Loney when he was 12 years old. He attributed heavenly inspiration/insights to the family Goddess Namagiri. He was an original and highly unconventional thinker, working in a difficult area of pure Mathematics called Number Theory. He proved approximately 3900 results - identities and equations.
16.6 Science - Panini (500BC) and the Development of Sanskrit Grammar
Panini formulated 3,959 rules of Sanskrit grammar known as Ashtadhyayi (meaning "eight chapters"). It is the most exhaustive as well as the shortest grammar of Sanskrit, or indeed, of any language. The grammars used to specify programming languages today are similar to Panini grammar rules, as acknowledged by the wellknown linguist Naom Chomsky.
16.7. Astronomers: the Early Mathematicians
Aryabhata (476-550 AD) used Mathematics(e.g., algebra (beej-ganit) and trigonometry (trikonmiti)) to understand the solar system.
He posited the axial rotation of the earth.
He inferred that the orbits of the planets were ellipses.
He deduced that the moon and the planets shined by reflected sunlight.
He explained the solar and the lunar eclipses.
He approximated pi (3.1416), the circumference of the earth (62832 miles) and the length of the solar year (within about 13 minutes of the modern calculation).
16.8. Varahamihira (505-587 AD) studied permutations and combinations, and provided a method of calculation of nCr that resembles the Pascal's Triangle. He also contributed to Astrology (in Sanskrit Encylopedia Brihat Samhita). Varahamihira is considered to be one of the nine jewels (Navaratnas) of the court of legendary king Vikramaditya (thought to be the Gupta emperor Chandragupta II Vikramaditya).
16.9. Brahmagupta (598-668 AD) did important work on the algebraic properties of integers, and solutions to linear, quadratic, and indeterminate equations. An indeterminate equation, in mathematics, is an equation for which there is an infinite set of solutions; for example, 2x = y is a simple indeterminate equation.
16.10. Bhaskar I (600 - 680 AD) used advanced mathematics to study ( understand and
predict ) conjunctions of the planets with each other and with bright stars; risings and
settings of the planets and the moon; positional number system with 0; pi as an irrational number; and formula for calculating the sine function. Bhaskara is apparently the first to write numbers in the Hindu-Arabic decimal system with a circle for the zero. (Different sources partition accomplishments of Brahmagupta and Bhaskara I differently because of the confusion caused by them being contemporaries.)
16.11. Sridhara (900 AD) provided mathematical formulae for a variety of practical problems involving ratios, barter, simple interest, mixtures, purchase and sale, rates of travel, wages, and filling of cisterns. He also studied arithmetic and geometric progressions, and formulas for the sum of certain finite series.
16.12. Satyendra Nath Bose: Of Boson Fame
Born: 1 January 1894, Calcutta, Bengal, India.
Died: 4 February 1974 (aged 80), Calcutta.
Achievement: FRS
Alma mater: Presidency College, Calcutta
Collaborators: Louis de Broglie, Marie Curie, and Albert Einstein. He has important contributions to modern physics, specifically Quantum Theory.Bose-Einstein Statistics,Bose-Einstein Condensate, and Boson(e.g., photon, meson, etc) are all named after him.
16.13. Sir Chandrasekhara Venkata Raman: Of Raman Effect Fame
Born: 7 November 1888, Trichi, Tamil Nadu, India.
Died: 21 November 1970 (aged 82), Bangalore.
Achievement: FRS
Alma mater: Presidency College, Madras
Doctoral Student: G. N. Ramachandran (Crystal Physics)
16.14. Sir C. V. Raman received the 1930 Nobel Prize in Physics for Raman Effect, which explains the Quantum Nature of Light. Specifically, Raman Effect explains the color of the sea is blue as the result of the scattering of sunlight by the water molecules. (Rayleigh Scattering, a different phenomenon, explains why the color of the sky is blue during the day and why the color of the horizon is red at sunset. It is due to a different reason: the result of the scattering of sunlight by the molecules in the air.) Further Reading - Tata Institute of Fundamental research has published a document outlining the contributions of the following distinguished scientists.
Prafulla Chandra Ray
Meghnad Saha
Satyendra Nath Bose
Shanti Swarup Bhatnagar
Homi Jehangir Bhabha
Subramaniam Chandrasekhar
Vikram Sarabhai
C. R. Rao
K. Chandrasekharan
Har Gobind Khorana
G. N. Ramachandran
Harish Chandra
M. K. Vainu Bappu
