Prof Raj Shree Dhar
Prime Minister Narendra Modi has often discussed India’s contribution to the field of Mathematics owing to our invention of Zero, and spoke about Vedic Mathematics during the 88th episode on his monthly radio address ‘Mann Ki Baat’.
Indian Knowledge Systems division is an innovative cell under Ministry of Education, in which the proposals for inter-disciplinary research in all subjects ranging from Art, Music, Dance, Drama, Indology to Mathematics, Astronomy, Science, Technology, Life science, Environmental sciences, Health, Yoga and other new fields have been invited.Rich heritage and traditional knowledge of Bharat about Vedas and Upanishads is also included.Research papers and books on the topic by leading thinkers are being prepared to develop Vision 2047 documenting a roadmap for establishing INS or Bharatiya Gyan Parampara based on the ancient and traditional Indian knowledge.Bharat has always boasted of a rich tradition in the area of learning and education since time immemorial. It is well known that people from other nations such as Europe, the Middle East, and Portugal came to Bharat to get a quality liberal education.
We come to know more and more about less and less. Once a scientist supposedly knew everything about atom; but atom has ramified into several branches like Electronics, Nuclear Physics, and Solid State Physics. Each specialist knows his own branch and cannot afford to know everything about other branches. Life before birth or after death, whether it is or isn’t, has to be investigated scientifically. The other alternative is to direct our gaze inwards and try the instruments of yoga to know more about the life after death although there is much Indian literature on this topic by the Saints and Munis of Bharat.
In Indian literature, Zero or Shuniya or Wheel of Creation is the most meaningful concept which has roots in Vedas and is beyond the concepts of space and matter.Shuniya is to be crossed for merger into super-conscious state of Turyateeta(yogic word), full of supreme bliss. A stage is reached when after constant practice of getting true knowledge, the aspirant is fit to enter into a region of Zero that is the region of absolute purity.Shuniya is of nature of nihility with respect to physical plane but it places at the feet of possessor the entire treasure of existence.Elliptical Lingum represents Shuniya and also Cosmos or Brahmand.There is no difference between zero and infinity like energy and holder of energy.Mahabindu, the great point where all existence stands with infinite power and glory, connects Zero to Infinity. Zero is represented by point or circle and one of its applications is Number theory practised widely in this world.
The form of our body is a great mystery and exploration of self is by Pratibigya, when we reach the fourth state of consciousness apart from three other states namely Wakeful, Sleep, and Dream. The 4th state is pure consciousness, enlightenment from central part of brain. The five functions related to Cosmos are creation, maintenance, destruction, dissolution and restoration.
In Indian Mathematics, someoldest mathematical records are perhaps the Sulba Sutras (dated variously between the 8th century BC and the 2nd century AD), appendices to religious texts which give simple rules for constructing altars of various shapes, such as squares, rectangles, parallelograms, and others. The Sulba Sutras give methods for constructing a circle with approximately the same area as a given square, which imply several different approximations of the value of ?. The four major Shulba Sutras, which are mathematically the most significant, are those attributed to Baudhayana, Manava, Apastamba and Katyayana. Their language is late Vedic Sanskrit, pointing to a composition roughly during the 1st millennium BC.
Vedic Mathematics deals mainly with 16 Vedic mathematical formulas or Sutras for carrying out tedious and complex arithmetical operations and to a very large extent, executing them mentally. The sutras are easy to understand, easy to apply and easy to remember and the time taken by these sutras will be less than the time taken by modern western methods.Panini (5th century BC) formulated the rules for Sanskrit grammar. His notation was similar to modern mathematical notation, and used meta rules and transformations. Acharya Pingala (3rd-1st centuries BC), ancient Indian poet and mathematician in his treatise of prosody uses a device corresponding to a binary numeral system. Pingala’s work also contains the basic ideas of Fibonacci numbers.
In the 5th century AD, Aryabhata wrote the Aryabhatiya, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology. Aryabhatta’s Aryabhatia (499 AD) includes the computation of areas and volumes. Brahmagupta wrote his astronomical work BrahmaSphutaSidhanta in 628 AD. Chapter 12, containing 66 sanskrit verses, was divided into two sections: “basic operations” (including cube roots, fractions, ratio and proportion, and barter) and “practical mathematics”.In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta’s identity and Brahmagupta’s formula, and for the first time, in Brahma- sphuta- siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu-Arabic numeral system. In the 12th century, Bhaskara lived in southern India and wrote extensively on all branches of mathematics known then. His work contained mathematical objects equivalent or approximately equivalent to infinitesimals, derivatives, the mean value theorem and the derivative of the sine function.
In the 14th century, Madhava of Sangamagrama, the founder of the so-called Kerala School of Mathematics, found the Madhava-Leibniz series, and, using 21 terms, computed the value of ? as 3.14159265359. Madhava also found the Madhava-Gregory series to determine the arctangent, the Madhava-Newton power series to determine sine and cosine and the Taylor approximation for sine and cosine functions.
Srinivasa Ramanujan, an Indian mathematician who made pioneering contributions to number theory was born on 22nd December, 1887. We celebrate the birthday of Srinivasa Ramanujan as the National Mathematics Day. In the words of Prof. Manjul Bhargava, the Fields’ Medal winner, “Ramanujan is a true national hero, a saint known to everyone”. Ramanujan saw things in Mathematics that no one could have even dreamt of seeing before. His story is incredibly inspirational and his place in Mathematics is huge and only grows every year as more of his work is understood. Speaking about Mathematics teaching in India, Bhargava admitted that it is robotic, and we have to make it creative and beautiful and that depends on how to teach it. This is definitely a Golden age for Mathematics in India and many more young people in India are eager to enter the field of Mathematics.
The Ramanujan Prize for young mathematicians from developing countries created in the name of Srinivasa Ramanujan, has been awarded annually since 2005. The Prize was originally instituted by the Abdus Salam International Centre for Theoretical Physics (ICTP), the Niels Henrik Abel Memorial Fund, and the International Mathematical Union (IMU). The participation of the Abel Fund ended in 2012; the 2013 Prize was jointly funded and administered by the ICTP and the IMU. The Prize is awarded annually to a researcher from a developing country, who must be less than 45 years of age on the 31st December of the year of the award, and who has conducted outstanding research in a developing country.
The students of today should be taught about the great Indian mathematicians like Panini, Aryabhatta, Bhaskara, Brahmgupta, Ramanujan and their literature written in Indian languages and also about the important breakthroughs in the history of Mathematics. It is always good to encourage our students to start thinking about numbers and their use in their own language(s)which comes naturally and comfortably to them.They should be trained in mathematical riddles, Brain teasers, Magical squares, Sudoku, Cards and Chess for logical thinking and improving concentration. Students should apply skills in estimating and calculating with whole numbers to solve and model everyday problems in a wide range of authentic contexts using efficient mental, written and digital strategies. They should be able to identify situations where money is used and apply their knowledge of the value of money to purchasing, budgeting and justifying the use of money. This element involves students developing an understanding of the meaning of fractions and decimals, their representations as percentages, ratios and rates, and how they can be applied in real-life situations.
Mathematical skills include constructing and clearly presenting mathematical and logical arguments, advanced numeracy skills, turning real world problems into mathematical problems, analyzing data, finding patterns and extracting solutions, thereby developing teamwork, leadership, and presentation skills. Mathematics can be offered as a joint honors degree paired with business management, computer science, economics, finance, sports science etc. There should be options to choose a foundation mathematics programme through various mathematical institutes offering research environments. Mathematics learning can be used as a sturdy foundation for nation-building since mathematical skills garnered from the stage of childhood itself go a long way in ascertaining the path a nation undertakes to become a global scientific and technological leader. Mathematics undoubtedly is going to play a crucial role in India’s growth story as an emerging superpower.
(The author is Principal, Govt. Degree College Purmandal, J&K)
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