Tuesday, April 01, 2014
Development of Mathematics in India
Sameena Tarannum, Reg. no. 1345302, Research Scholar, Christ University
A Philosopher and Mathematician René Descartes (1596-1650) said "Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency."
Mathematics is generally presented 'ready-made' to students with procedures, methods and applications in systematic and logical order. However, like any other academic subject, Mathematics also has a history which is rich in astonishing inventions and breakthroughs. This history gives a narrative and human context which adds colour and context to the discipline.
Starting from the representation of numbers, through the methods of arriving at the solutions of unknown equations, to the expansion of classy techniques in managing the inﬁnite and the inﬁnitesimals, there has been an extensive variation in the choice of approaching, visualizing and understanding the problems and solutions amongst the Mathematicians.
Mathematics in India has a very extended and consecrated history. Sulbasutras, the oldest existing texts (prior to 800 BCE) clearly state and make use of the so-called Pythagorean theorem. By the time of Aryabhata (c. 499 CE), the Indian Mathematicians were fully acquainted with most of the Mathematics that we currently teach at the elementary level in school. Starting with Aryabhata in the 5th century and extending up to Narayana Pandita of the 14th century, the Indian Mathematicians have blazed a trial in the study of several branches of Mathematics that include obtaining recurrence relation for the construction of sine table, ﬁnding solutions to unknown equations.
In the valley of the Indus river of India, the world's oldest civilization had developed its own system of Mathematics. The Vedic ShulbaSutras show that the earliest geometrical and Mathematical inquiries amongst the Indians arose from certain requirements of their religious rituals. Although Vedic mathematicians are known primarily for their computational genius in Arithmetic and Algebra, the basis and inspiration for the whole of Indian Mathematics is geometry. The beginnings of algebra can be traced to the constructional geometry of the Vedic priests, which are preserved in the ShulbaSutras.
The aim of this essay is to present a critical overview of Mathematics education in higher education level in India which typically refers to Mathematics taught at the undergraduate and post-graduate levels and would also cover research Mathematics. By focusing primarily on undergraduate Mathematics education and by generalizing from different experiences I hope to throw some light on curriculum and pedagogy in Mathematics. Only a tiny fraction of the Indian population (1.2 billion strong) enters higher education and is expanding rapidly over a last decade. India is therefore faced with the triangle of quality, quantity and equality.
India has the third largest higher education system in the world (after China and the USA) suggests that there is a great deal of Mathematics around as well. India is also home to some institutions where world class research in Mathematics is carried out. A sturdy group of Indian Mathematicians have been contributing to the growth of many areas of Mathematics. The legendary genius Srinivasa Ramanujan has inspired and stimulated generations of young Indians towards taking up Mathematics as a calling.
In twentieth century, Mathematical Sciences is growing exponentially. In India, the growth of Mathematical Sciences has not been less spectacular. In the first three decades of this century, only one university, namely, Calcutta University was producing PhD theses and today about a hundred of universities are producing PhDs in Mathematics. In fact, during the first twenty five years of its existence, IIT Kanpur has produced about three times the number of these produced by the entire country in the first five decades of this century.
As mentioned, the first set of theses came from Calcultta University and then followed by Madras University and this had to do great deal with the founding in the Indian Mathematical Society in 1907 which had its headquarters in Madras. However, solemn research started in the year 1927. In this period, we had Ramanujan from Madras University who contributed a lot to the world as a well-known Mathematician.
The credit for starting research in North India goes to Ganesh Prasad who brought some inspiration for it from Calcutta University where he had served as Professor of Applied Mathematics during 1914-1917. He then continued his teaching in Benaras Hindu University from 1917 to 1923 and gave new crescendos to research and founded Benaras Mathematical Society which was renamed to Bharat Ganit Parishad. Bombay University was started at the same time as Calcutta and Madras universities but it produced its first PhD thesis in Mathematics in the year 1942.
The Indian Statistical Institute also contributed to the development of Operations Research in India by Prof. Mahalanobis. Two other centres Defence Science Organisation and Delhi University laid research in the same field and this led to the founding of the Operations Research Society of India. Research in Applied Mathematics developed greatly due to the starting of five Indian Institutes of Technology, the strengthening of Mathematics departments in regional colleges of engineering and the setting up of the Department of Applied Mathematics in Indian Institute of Science at Bangalore.
The most prestigious school of Mathematics is at the Tata Institute of Fundamental Research (TIFR), Bombay. During more than four decades of its existence, this school has done tremendous work of international standards in many areas of pure Mathematics.
All these universities have contributed immensely and these have laid a foundation to the development of Mathematics in all the universities in India.