Going by our modern understanding of mathematics, it may be assumed that the history of the same would then have to be very straightforward. In this regard, an ordinary person would undoubtedly attribute the developments of mathematics to calculators and computers. However while we acknowledge the dynamics and fundamentals in the world of mathematics, we constantly ignore some of the most significant developmental factors that led to great mathematical discoveries such as multiplication, the ten numerals or even the fact that zero is considered a numerical figure.
The perception in which we view the development of mathematics is necessitated by the fact that the society we live in currently dictate that we learn mathematics within the shortest time possible and be able to comprehend the same within a set time frame. However, this is not the same case with mathematicians. These people discovered mathematical principles through knowledge building and the societies in which they lived. This is one of the main reasons we are taught that most of these people learn mathematics through trial and error. What may have appeared to be small steps in the development of mathematics have become the foundation in which mathematics is based in modern day world.
Let's start with the ten numerals that we commonly use in our everyday life. It is a fact that the system cannot be said to be standard in all regions. Even in America, there are over ten ways of writing the numerical values. There is the system with 0 1 2 3....9 and there is of course the tallying system of the grouping system that is used to tally things such as scores. Different cultures on the other hand developed different numerical systems with the Romans adopting the use of consecutive symbols. Other nations went ahead and developed symbols just like the Romans such as the Chinese and the Mayans. Despite all these steps towards the advancement of mathematics, multiplication is considered as the missing link that was required to ignite the complex nature of mathematics as it is today. It was found out that for mathematics to advance further, there was a need to develop a more complex system of integration of numbers.
The historical development can be traced in major periods in the evolution of mathematics whereby different periods exhibited different and distinctive characteristics with respect to mathematics.
The earliest period in the evolution of mathematics is what is known as Proto-mathematics. This early period mathematics exhibits the characteristics of being a product of empirical observations and individual interactions with the general environment. Mathematics started from man's basic mathematical understanding such as counting, symmetry in art and craft, measuring and building. The evolution of man to an even more settled lifestyle saw the development of more complex mathematical procedures. There was the development of hierarchies and the growth of administration which necessitated the need for the preservation of the knowledge that man had learnt over the years.
The Proto-mathematics was followed by ancient mathematics. This came as a result of the extremely sophisticated science by both the Egyptians and Babylonians. During this period, the said cultures applied astronomy, time regulation, land surveying, logistical analysis and engineering which in one way or another involved the discipline of mathematics. During this period, mathematics was viewed as a phenomenon of numbers as compared to being a respective discipline. According to George (1991, pp.140—148), It is amazing how the mathematics at this time of both of these two cultures was complex. surprisingly accurate astronomical computations, the value of to several decimal places, formulas for areas of a number of two- and three- dimensional objects, knowledge of structural stability and its manifestation in wondrous architecture are just but some of the mathematical advancement of this period. The advances in mathematics in this era proved to be very essential in helping out such processes as administration of taxes, surveying and planning, record maintenance and other management process of both people and data.
The ancient mathematics was followed by the early classical mathematics. One of the most significant characteristic about the early classical mathematics is that the mathematical procedures during this period incorporated more complex procedures such as empirical arrangement, geometry and axioms. In general, mathematics was assumed to be a formal structure held together by various laws of thought.
In Europe, different concerns from modern mathematicians drove the interest in mathematics. The belief that mathematics was the key to understand nature was the major element driving interest. In the Renaissance period, mathematics as well as accounting was interrelated. The modern advances in mathematics have become common, which lead to the ignorance of fundamental developments like multiplication among others. The culture and period that we live in influences the way we view mathematics and other difficult concepts.
Throughout history, mathematics has discovered some principles in different orders. They have discovered through building knowledge and the wisdom that is inherited from which the mathematical as well as the numerical systems are found in, and motivations that certain cultures have provided.
Mathematics has been learnt from books, and professionals who developed it through both trial as well as error. Small steps of many people from the many different cultures in years direct this development and not through big leaps by bright individuals. This development in mathematics is viewed according to people's way of understanding and its sophistication. No other methods other than appreciating difference in the viewpoint and of the one of mathematics in the past. Often, the method used to teach mathematics today makes it difficult to comprehend the difficulties experienced in the past.
Mathematics is perceived by some people to be boring as well as irrelevant, but it is actually highly applicable and valuable by industries and in science. The negativity of mathematics crops up a circle, which puts the young people not to study mathematics at the university. This creates lack of informed teachers and professionals, therefore promoting this negative image.
Mathematics being a mysterious subject, it has several myths associated with it. These myths are widespread and are present worldly among different people. Moreover, these myths are mostly negative. These negative images are the reasons that lead to the decrease of students enrolling in mathematics and various subjects that are associated with it such as sciences. Over the years, many people describe mathematics as a process to learn. For example, mathematics is a skill that one need to learn, solve the problem, and explain the physical process. Other people indicate that it is a process that is hierarchical, where one theory results to another which involves logical thinking. It is also viewed as mental work which tests the mind.
Mathematics is related to many other views which describe it as a process involving hard work or an effortful endeavor that requires concentration that satisfies when it is right. Studies show that many students enroll in mathematics since it is career oriented and marketable to achieve in future. It is seen as a tool that needs practice or a science of study. All these views that are associated to mathematics are related to its content.
However, human interests play a key role in making choices in problems concerning mathematics, and concepts. In the development of mathematics, mathematicians chose definitions worth pursuing. Currently, the upsurge of mathematics that is related to computers show a significant shift of values that are linked with technological developments manifested in knowledge. Mathematics can be viewed as value free, whereby the values are made as a choice of norms as well as rules. Philosophies on mathematics have certain concerns regarding it as an objective subject that is free of ethics and other values. Some view it as value-neutral and only concerned with structures.
Any possible intrusion of values is either regarded as an inessential flourish or as a misrepresentation of the subject caused by human fallibility. Claims displayed implicitly by mathematicians are not disregarded by mathematics philosophies. Besides, mathematics is acknowledged to have preferences and values that are seen in their activities in mathematics. Thus, the values shaping mathematics are not subjective or needed results of studying the subject.
Career prospects and mathematics applications motivate people to study the subject. For mathematicians, the beauty of the ideas, facts, and the quest to find the truth fascinates them. People need to recognize that the development of mathematics has a high value in all aspects of learning. To improve the general view of mathematics, mathematicians should engage the public in promoting the subject. Mathematics is a vital subject that is important in all learning aspects regardless of the criteria.
In conclusion, mathematics has come a long way to become the complex discipline that it is today. Some of the people that contributed to the significant development in the discipline have long been forgotten but their tremendous efforts have turned around the public perception of the discipline. Previously, mathematics was viewed as a formal structure held together by various laws of thought. According to Aaboe, There are many observable trends in mathematics, the most notable being that the subject is growing ever larger, computers are ever more important and powerful, the application of mathematics to bioinformatics is rapidly expanding, and the volume of data to be analyzed being produced by science and industry, facilitated by computers, is explosively expanding (1998)
Aaboe, Asger (1998). Episodes from the Early History of Mathematics. Random House: New York.
Melville J. Duncan (2003). Third Millennium Chronology, Third Millennium Mathematics. St. Lawrence University: New York
George Gheverghese Joseph, (1991) The Crest of the Peacock: Non-European Roots of Mathematics, Penguin Books, London, pp.140—148
Robert Kaplan, (1999) "The Nothing That Is: A Natural History of Zero", Allen Lane/the Penguin Press: London
Rudman, Peter Strom (20007). How Mathematics Happened: The First 50,000 Years. Prometheus Books. p. 64