# History, Sociology, and Philosophy of Mathematics

## Abstract

Mathematics is a universal subject in the 21st century. In spite of its popularity, a significant proportion of the population cannot even define it. However, people have not failed to realize its importance in our everyday life given that it has played a considerable role in many inventions. Understanding the history of mathematics allow us to appreciate the efforts that our ancestors made for us to benefit from the present math which is nothing new but rather a modification of the ancient one. Another important element that is highlighted in the history of mathematics is the approval that there is a connection between the discipline and other fields. Acknowledgment of the interrelationship has significantly contributed to the expansion of the knowledge as well as the popularity of mathematics. The 21st century has seen illiterate communities embrace the role of the subject which means the knowledge has diffused from European and Islamic regions to other continents such as Africa. Establishment of a multicultural approach to improving the concepts of mathematics has transformed our perceptions regarding the subject. For instance, unlike in the earlier centuries, people calculated sums on a piece of paper, this has changed since as devices are being used to ease the work involved.

## Introduction

As the years passes the relationship between humanity and technology is progressively becoming intense. According t

...o Heidegger, the firm connection has made people obsessed with inventions and innovation; this has made us subjects to technology as we are aligning every aspect of our lives in a way that will allow us to discover more developments. In spite of the multiple criticisms, it will be untrue to demonize technology given the enormous changes it has brought which have significantly improved our lives. Therefore, demanding for the logic behind any idea is no longer surprising in the 21st century where everyone wants an in-depth understanding of new concepts that often form the basis of advancements. As much as scholars can use available theories to explain their notions, the principles are always highlighted in a quantitative manner. The recurrence of such incidences is an implication that mathematics is at the center of all developments regardless of the varying disciplines.

Mathematics is a science that involves the orderly operation of quantities to establish a connection between numbers and properties. The discipline is has two broad categories that are pure and applied mathematics. Pure mathematics is governed by the rules of the discipline because its objective is limited to finding an appropriate answer for a question through devising solutions and finding pieces of evidence that can prove the underlying facts. On the other hand, applied mathematics is directed towards solving environmental issues. Strategies for the search for solutions are often aligned by the matter at hand and therefore, it can deviate from the standard principles of mathematics. Over the years, the misconception that developments arise from actual science has been gaining grounds globally. Such misleading assumptions can be attributed to the belief that limits development to tangible materials such as computers. People often fail to notice the role that socia

sciences play in these advancements.

Given that mathematics is at the core of technological advancements, understanding its history and evolution will not only enable us to appreciate its importance but might also give us a glimpse of what we can expect in future. Having an understanding of the correlation between social sciences i.e. philosophy and sociology and mathematics is the only way for us to realize such a dream. Most academicians are abandoning the old notion that treated social sciences and mathematics as incredibly separate disciplines that could not be associated in any manner. The progress has resulted to the development of new disciplines such as philosophical mathematics, sociological mathematical and ethnomathematics. The first one aims to expound the knowledge concerning the connection between quantities and properties. Therefore, it explains foundations, assumptions, and implications of mathematics. The second field deals with the impacts of mathematics to human interrelations while the last branch ethnomathematics tracks and evaluates popularity and advancement of mathematics in a multicultural society. History also tends to correlate with sociology as well as philosophy. History uncovers past events while sociology concerns itself with present day events. Therefore, history can be considered past sociology and sociology the current history. Additionally, philosophy explains general human relations and their surroundings. The review examines the trends in the history, pattern and philosophy of mathematics by Tinne Hoff Kjeldsen.

## Discussion

According to O’Connor and Robertson (O’Connor & Robertson, 1997), it is impossible to accurately state when mathematics was invented; this is because the present history is dependent on evidence that historians were able to cover. Therefore, only the recorded information was considered which leaves out the basics that had been discovered before our ancestors had formulated ways to keep some form of documents. The ancient mathematics involved dealing with abstract numbers that people applied to their daily activities. Like any other advancements, the ancient mathematics establish a base from which further developments were carried out over time to give rise to the present day complex but simplified mathematics. After the prehistorical era, various empires developed the ideas of numbers further. For instance, the Babylonians mathematics used the notation table system with a number radix of sixty; they formulated some basic formulas that could represent large random numbers as well as fractions. Such a significant step paved way for the advancement of more sophisticated mathematical methods, for example, Pythagorean triples which involve the use of letters to represent figures as well as linear and quadratic equations.

The Babylonians mathematics ideologies were inherited by the Greeks who made some considerable developments. One significant achievement that the Greeks discovered was the knowledge that rational figures could not measure all lengths; this led to the formulation of irrational digits that could cater for the lengths that did not fit into the natural numbers. Later on, scholars discovered the irrational figures could be used to establish the size of a particular surface which is the present day area. Although pure mathematics was common at that time, people began reasoning beyond the scope of the field’s principle which gave rise to applied mathematics (Cooke, 2012). For instance, the quest to uncover the

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