### Wednesday, April 26, 2006

## Hindu mathematicians' contribution

Hindu mathematicians' contribution

Many people think mathematics as basic computational skills but it is much more than that. It is the language of science. Mathematics is a way of thinking, a way of organizing, analyzing, and synthesizing a body of data. It uses carefully defined terms and symbolic representation that enhance our ability to communicate. Many scholars view mathematics as an organized body of knowledge in which each proposition follows as a logical consequence of proved proposition or assumptions. In other words, we can say that mathematics is a body of knowledge in the area of science, with its own symbolism, terminology, contents, theorems and techniques. It can be broadly classified as pure and applied mathematics. However, mathematics education itself is an applied discipline.

Number is one of the basic concepts of mathematics. Its origin dates back to ancient times. Human society created or invented the counting numbers by developing it through practices. Or, we can say, man developed counting numbers in order to concretize the idea or notion he got through the matching (e.g., laying aside a stone for each cow) and while considering the order of occurrence of some events. Many kinds of numbers are known today. In fact, they were not discovered or created simultaneously. Of all the kinds of numbers, the counting numbers are certainly the first ones to be used by human society.

The counting numbers- also known as natural numbers- is probably the simplest and most familiar numbers known to us. Although the notion of counting numbers is a universal one, these are called by various special names or number-names by different people in different parts of the world. Similarly, these numbers are represented by different symbols or numerals such as "1" in Hindu-Arabic system, "!" in Devanagari script, "I" in Roman system, and "▼" in Babylonian system. That is, there are many ways of using counting number symbols or numerals (system of numeration) to represent numbers.

The Devanagari system of numeration (), !, @, #, $, %, ^, &, *, () and the Hindu-Arabic system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are practically one and the difference is only of the written script or lettering. Here, the ten number symbols are used and hence each of these systems is known as a "base ten system". The number zero, denoted by "0", is one of the most valuable contributions of the Vedic Hindu mathematicians. This number had been used by Pingal in his famous book Chhandasutra, which was written in two century before Christ. Even great mathematicians of the West hesitated to accept it as a number for a long time. The traditional Western number system, that is the Roman system of numeration uses the Roman letters and their combinations to represent various numbers. There is no counter part of the number symbol "0", called zero, in the Roman system. Similarly, there is no symbol for "zero" in Babylonian as well as Egyptian number system too. Without this "0", the digital world could not be developed. As we know, a computer, essentially, is a machine that can process, store and retrieve information and it understands every data in terms of either "0" or "1".

Mathematics should be a central part of the curriculum. As stated by Mathematics Association, London, there are experiences that the education should provide: a sense of culture and history, the development of skills, a climate that encourages inquiry, opportunities to discover and develop individual talents, a sense of community and of the worth of the individual within it, the enjoyment that comes with sustained creative effort, opportunities for both individual action and co-operation, a perspective which keeps these elements in balance. Mathematics can play a major role in contributing to all of these aspects. In some areas the role of mathematics is pre-eminent. The power of mathematics can be demonstrated in many ways. Mathematics is empowering and is fundamental to the study of other subjects. It is both an essential part of the world's intellectual and cultural heritage and the door to its scientific and technological future. There is a much wider need for mathematical skills; every day life as well as science and engineering, production management, and investment decisions are just a few example which illustrate our dependence on these skills.

In Nepali context, though much emphasis has given to mathematics education, we are studying it as a borrowed subject. In fact, since Nepal is the inheritor of culturally rich civilization having a history of thousands of years a tradition of mathematics education, rich and refined both in theory and practice, has been an inseparable part of our culture and civilization. There are numerous achievements of our ancestors in the field of mathematics. As mentioned above, the number zero, denoted by "0", is one of the most valuable contributions of the Vedic Hindu mathematicians. Do our students know the fact that methods of Square Root and Cube Root also were invented or developed by Vedic Hindu mathematicians? The method of solving Equation has developed by Hindu Brahmins in more than three centuries before Christ and it was brought to Europe in 1668 A.D. Hindu mathematicians Varahmihir and Lalla had used the value of "Pi" (which is equal to 3.1416) in 505 and 578 A. D. respectively. Great Hindu mathematician Aryabhatta had determined this value previously. Do our students know these facts? If we read a Hindu text Shulbasutra, which was written in eight centuries before Christ, vast knowledge of Geometry is there. The famous Pythagoras theorem is actually suitable to call "Baudhayan theorem" because it had been propounded by Hindu saint Baudhayan much before than the birth of mathematician Pythagoras. It is injustice not to give renown to our ancestors (Vedic Hindu mathematicians) for their contribution in the field of mathematics. While teaching mathematics in our schools and universities, we must inform our pupils to such facts too.

Many people think mathematics as basic computational skills but it is much more than that. It is the language of science. Mathematics is a way of thinking, a way of organizing, analyzing, and synthesizing a body of data. It uses carefully defined terms and symbolic representation that enhance our ability to communicate. Many scholars view mathematics as an organized body of knowledge in which each proposition follows as a logical consequence of proved proposition or assumptions. In other words, we can say that mathematics is a body of knowledge in the area of science, with its own symbolism, terminology, contents, theorems and techniques. It can be broadly classified as pure and applied mathematics. However, mathematics education itself is an applied discipline.

Number is one of the basic concepts of mathematics. Its origin dates back to ancient times. Human society created or invented the counting numbers by developing it through practices. Or, we can say, man developed counting numbers in order to concretize the idea or notion he got through the matching (e.g., laying aside a stone for each cow) and while considering the order of occurrence of some events. Many kinds of numbers are known today. In fact, they were not discovered or created simultaneously. Of all the kinds of numbers, the counting numbers are certainly the first ones to be used by human society.

The counting numbers- also known as natural numbers- is probably the simplest and most familiar numbers known to us. Although the notion of counting numbers is a universal one, these are called by various special names or number-names by different people in different parts of the world. Similarly, these numbers are represented by different symbols or numerals such as "1" in Hindu-Arabic system, "!" in Devanagari script, "I" in Roman system, and "▼" in Babylonian system. That is, there are many ways of using counting number symbols or numerals (system of numeration) to represent numbers.

The Devanagari system of numeration (), !, @, #, $, %, ^, &, *, () and the Hindu-Arabic system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are practically one and the difference is only of the written script or lettering. Here, the ten number symbols are used and hence each of these systems is known as a "base ten system". The number zero, denoted by "0", is one of the most valuable contributions of the Vedic Hindu mathematicians. This number had been used by Pingal in his famous book Chhandasutra, which was written in two century before Christ. Even great mathematicians of the West hesitated to accept it as a number for a long time. The traditional Western number system, that is the Roman system of numeration uses the Roman letters and their combinations to represent various numbers. There is no counter part of the number symbol "0", called zero, in the Roman system. Similarly, there is no symbol for "zero" in Babylonian as well as Egyptian number system too. Without this "0", the digital world could not be developed. As we know, a computer, essentially, is a machine that can process, store and retrieve information and it understands every data in terms of either "0" or "1".

Mathematics should be a central part of the curriculum. As stated by Mathematics Association, London, there are experiences that the education should provide: a sense of culture and history, the development of skills, a climate that encourages inquiry, opportunities to discover and develop individual talents, a sense of community and of the worth of the individual within it, the enjoyment that comes with sustained creative effort, opportunities for both individual action and co-operation, a perspective which keeps these elements in balance. Mathematics can play a major role in contributing to all of these aspects. In some areas the role of mathematics is pre-eminent. The power of mathematics can be demonstrated in many ways. Mathematics is empowering and is fundamental to the study of other subjects. It is both an essential part of the world's intellectual and cultural heritage and the door to its scientific and technological future. There is a much wider need for mathematical skills; every day life as well as science and engineering, production management, and investment decisions are just a few example which illustrate our dependence on these skills.

In Nepali context, though much emphasis has given to mathematics education, we are studying it as a borrowed subject. In fact, since Nepal is the inheritor of culturally rich civilization having a history of thousands of years a tradition of mathematics education, rich and refined both in theory and practice, has been an inseparable part of our culture and civilization. There are numerous achievements of our ancestors in the field of mathematics. As mentioned above, the number zero, denoted by "0", is one of the most valuable contributions of the Vedic Hindu mathematicians. Do our students know the fact that methods of Square Root and Cube Root also were invented or developed by Vedic Hindu mathematicians? The method of solving Equation has developed by Hindu Brahmins in more than three centuries before Christ and it was brought to Europe in 1668 A.D. Hindu mathematicians Varahmihir and Lalla had used the value of "Pi" (which is equal to 3.1416) in 505 and 578 A. D. respectively. Great Hindu mathematician Aryabhatta had determined this value previously. Do our students know these facts? If we read a Hindu text Shulbasutra, which was written in eight centuries before Christ, vast knowledge of Geometry is there. The famous Pythagoras theorem is actually suitable to call "Baudhayan theorem" because it had been propounded by Hindu saint Baudhayan much before than the birth of mathematician Pythagoras. It is injustice not to give renown to our ancestors (Vedic Hindu mathematicians) for their contribution in the field of mathematics. While teaching mathematics in our schools and universities, we must inform our pupils to such facts too.

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