Questions and Answers
1. The beginning of mathematics dates back to any civilization ever formed, which developed a form of writing. Use of numbers, shapes and basic mathematical operations could be seen in almost every civilization, in the form of quantification in crafts, trade and work. On studying construction sites, anthropologists could clearly conclude that some amount of mathematical understanding prevailed in the people.
Evidences found in the rectangular bases of buildings, in the designs of weaving patterns, basketry; craft etc. all prove that there existed an understanding of mathematics even in early civilizations. In about 500BC, trade and tax laws were formulated in the Ancient Near East. These laws made use of simple mathematical modeling to be formulated. In the 19th century, Egyptian papyrus samples obtained by archaeologists showed an understanding of mathematics, especially multiplication. Use of tens and ones in the form of symbols, usage of addition by doubling method, use of fractions, simple linear equations and computation of areas and volume of a wide variety of geometrical shapes, are only some of the features of Egyptian mathematics. Tablets obtained from the Old Babylonian period give evidence of math usage in administration, training and learning. Mathematics in India is said to have been formulated in around 600BC, with excessive mention of the Pythagoras Theorem, surface area of volume and solids. Greek mathematicians used logical reasoning and proof as a basis of calculations which emerged as early as 600BC. Concept of whole numbers, ratios, mechanics and astronomy, could be seen as clearly in their knowledge of math.
It is evident that mathematics emerged at a very early age, even as man was establishing civilizations. These evidences are however, only in accordance with history, but mathematics has existed in the universe even before man was born. The timing of rotation and revolution of planets and celestial bodies, geographical calculations, physical and chemical proportions, atomic structure and even multiplication of microorganisms, all make use of math knowingly or unknowingly.
2. Yes, there exists a wide gap between ‘pure’ and ‘applied’ mathematics in our lives today. Such instances can be seen even in the past, after the advent of mathematics into human civilizations. The Old Babylonian period consisted of mathematical activities that arose due to daily necessities. Later on, immense interest in the subject, led people to delve deeply into mathematical problems, without actually looking at its practicality. The stress was laid more on solving complex mathematical problems than on its practical application.
Several advancements were taking place simultaneously in the world when there seemed to be a mathematical revolution. New ideas, axioms, postulates and theorems cropped up though there was not much of collaboration between countries. Chinese mathematics consisted of a formal set of solutions for several problems without actually giving its theoretical proof. The same applied to Greek mathematics. There was no stringent line between ‘pure’ an ‘applied’ mathematics. For instance in theoretical mathematics, line segments and their properties were mentioned, but the existence of different lengths of a line segment was not. However, in practical situations, line segments with different lengths were used. There was a change during mathematicians such as Plato, Aristotle and Euclid, when they began to see the importance of practical reasoning along with theorems and axioms. Applications of theories to one’s lives were the main theme of the 18th century mathematicians. Scientists such as Newton, Bernoulli and Leibnitz worked intensely to achieve this purpose. Leibnitz believed that mathematical calculations need to be done without actually bothering about the theory or postulates. Euler was another great mathematician who rediscovered and redefined mathematical theories and applied them in designing ships and turbines. He also popularized calculus. Laplace and Lagrange also stressed on practical applications, so much so that Lagrange felt that diagrams were no longer needed.
The 18th century mathematicians laid a strong foundation for upcoming research studies in mathematics. They believed that practicality should be the priority over theorems and postulates. They were a turning point in the history of mathematics.
3. I agree that mathematics has evolved precisely as a symbolic counter part of the universe. I state this on analyzing the prevalence of mathematics, not only in our world but the whole universe. Mathematics is not an invention but a discovery just as science is. Mathematics and science are closely related to one another. So is their concept of existence and exploration. Like science needs to be explored, mathematics too, was discovered on exploration.
Even before man existed and when the universe was differentiated into planets, stars and other celestial bodies, mathematics existed. It exists in calculation of rotation, revolution, constant orbiting of planets around the sun etc. Mathematics also exists in the blanket of atmosphere surrounding the earth in its calculated layers. It exists in stretches of geographical locations, in weather and in climate. Even before man could find out what mathematics is, seasons changed at fixed intervals of time, and day and night occurred alternately. The first life form on earth which was a single-celled organism also multiplied in a mathematical way. The rule of mathematics is universal and applies to all bodies big and small. No wonder, mathematics works so well with our lives, always surrounding us in different circles of life.
It can be rightly said that the universe has imposed mathematics upon humanity even before humans were created. There is no escaping it. It was invented only when man realized that mathematics existed. There is hardly any field on this earth which can survive without the support of mathematical branches.
Work Cited
Berlinghoff, William.P, and Gouvea, Fernando.Q. Math through the Ages: A Gentle History for Teachers and Others. The Mathematical Association of America: Oxton Publishers, 2004. Print.
