Mathematics In India Past Present And Future 64126u

MATHEMATICS IN INDIA PAST PRESENT AND FUTURE INTRODUTION

Mathematics is the science to which the Indians have contributed the most. But Indian mathematics has not been given the credit or recognition that it deserves. Many of the foundational concepts used in all mathematics were first discovered by the Indians. The most fundamental contribution of ancient India in mathematics is the invention of decimal system of enumeration, including the invention of zero(????). The developments that we see today aren’t possible without our basic concepts. Yet the condition of present Indian mathematics is very poor. We haven’t made any noticeable achievements in this present generation. So in this condition it is very sad to say that future of Indian mathematics is in danger. Today through this seminar I’m presenting that “what was the past of Indian mathematics, how is its condition now &what will be its future?

INDIAN MATHEMATICS IN PAST

According to their duration of periods it can be divided as follows:      

INDUS VALLEY MATHEMATICS (C. 2300 TO 1700 BC) MATHEMATICS IN THE AGE OF VEDAS (2000 BC-800 BC) THE AGE OF THE SUTRA PERIOD (800 BC-200 BC) JAIN MATHEMATICS (C. 600 BC TO AD 300) PRE-CLASSICAL AGE OF EPICS ANDSIDDHANTAS (200 BC-AD 320) THE CLASSICAL PERIOD (AD 320-750) MATHEMATICS IN THE MODERN AGE

There had been made many contributions to mathematics during each of these periods. But they didn’t get publicity because most of their written s were in Sanskrit which was known only to a few people. There are a lot of facts to say about each of these divisions but due to my time limit I’m starting with the CLASSICAL PERIOD OF INDIAN MATHEMATISM.

It was through brilliant mathematicians that this period was known. The most prominent mathematicians during this period were AryabhataI ,Brahmagupta and BhaskaraII. ARYABHATA

Aryabhata (475 A.D. -550 A.D.) is the first well known Indian mathematician. In the section Ganita (calculations) of his astronomical treatise Aryabhatiya (499 A.D.), he made the fundamental advance in finding the lengths of chords of circles, by using the half chord rather than the full chord method used by Greeks. He gave the value of as 3.1416, claiming, for the first time, that it was an approximation. (He gave it in the form that the approximate circumference of a circle of diameter 20000 is 62832.) He also gave methods for extracting square roots, summing arithmetic series, solving indeterminate equations of the type ax -by = c, and also gave what later came to be known as the table of Sines. He also wrote a text book for astronomical calculations, Aryabhatasiddhanta. Even today, this data is used in preparing Hindu calendars (Panchangs). In recognition to his contributions to astronomy and mathematics, India's first satellite was named Aryabhata. BRHMAGUPTA

Brahmagupta (598 A.D. -665 A.D.) is renowned for introduction of negative numbers and operations on zero into arithmetic. His main work was Brahmasphutasiddhanta, which was a corrected version of old astronomical treatise Brahmasiddhanta. This work was later translated into Arabic as Sind Hind. He formulated the rule of three and proposed rules for the solution of quadratic and simultaneous equations. He gave the formula for the area of a cyclic quadrilateral as where s is the semi perimeter. He was the first mathematician to treat algebra and arithmetic as two different branches of mathematics. He gave the solution of the indeterminate equation Nx²+1 = y². He is also the founder of the branch of higher mathematics known as "Numerical

Analysis". BHASKARA

Bhaskara (1114 A.D. -1185 A.D.) or Bhaskaracharaya is the most well known ancient Indian mathematician. He was the first to declare that any number divided by zero is infinity and that the sum of any number and infinity is also infinity. He is famous for his book Siddhanta Siromani (1150 A.D.). It is divided into four sections -Leelavati (a book on arithmetic), Bijaganita (algebra), Goladhayaya (chapter on sphere celestial globe), and Grahaganita (mathematics of the planets). Leelavati contains many interesting problems and was a very popular text book. Bhaskara introduced chakrawal, or the cyclic method, to solve algebraic equations. Six centuries later, European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it "inverse cyclic". Bhaskara can also be called the founder of differential calculus. He gave an example of what is now called "differential coefficient" and the basic idea of what is now called "Rolle's theorem". Unfortunately, later Indian mathematicians did not take any notice of this. Five centuries later, Newton and Leibniz developed this subject. As an astronomer, Bhaskara is renowned for his concept of Tatkalikagati (instantaneous motion).

There were many mathematicians during this period but through the contributions of these three people itself we will get ideas about our past in mathematics .After this period the greatest mathematician produced in India was Sreenivasa

Ramanujan. His period was included in the modern age of Indian mathematics. SRINIVASA RAMANUJAN

Srinivasa Aaiyangar Ramanujan is undoubtedly the most celebrated Indian Mathematical genius. He made extraordinary contributions to the theory of numbers, including the partition function and the theory of modular functions.