History, Sociology, and Philosophy of Mathematics Essay Example

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 social 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 mystery of the space i.e. celestial objects and the physical universe which led to trigonometry.
Development had proceeded smoothly from the prehistoric period to the Greek era. However, a stagnation was witnessed between 300BC and 200Bc where the West seemed contended with what had already been invented. At the same time, Islamic countries such as Syria and Iran were making some significant progress that was based on what the Greeks had already attained. In

the 11th century academicians like Adelard and Fibonacci introduced the Islamic developments in Europe. For almost four centuries no considerable modifications were made; this stagnation can be attributed to the period that people often take to accept, internalize and comprehend new ideas before discovering weak points that they can improve. However, the 16th century marked the end of the dormancy that had lasted for almost four hundred years; the algebraic solutions were expounded by the formulation of techniques that could solve quartic and cubic equations. Unlike the previous inventions which were limited to a particular region i.e. where they had been discovered, algebraic discovery spread in most of the world. The popularity attracted the interest of a good proportion of the population; this created positive perceptions as people started realizing the importance of mathematics in solving environmental problems.

The 17th and 18th century’s developments include the discovery of mathematical concepts such as calculus, probabilities, and logarithms. The ideologies shaded some light concerning the connection between mathematics, astronomy, and physics. The information led to the formulation of the theory of light and gravity by Isaac Newton. The 17th century would have seem more developments but several aspects acted like impediments. For instance, Thomas Hobbes proposed that lines contain some tiny points that could not be measured which he called infinitesimal. However, he faced great resistance from religious leaders who denounced any attempts to explain nature. Other than the Church Hobbes ideas were rejects by physicists such as John Wallis on the grounds that Hobbes notion lacked proof (Baron, 2014). There was rapid progress in the 19th century such as the algebra was expounded to encompass synthetic and

analytical geometry. Further innovations were subsequently made according to previous mathematical principles and the environmental issues of the moment. However, the misconception that classified mathematics and social sciences as extremely different fields and thus rejected any form of interactions acted as impediments to technological advancements. The treatment of math and other subjects limited people’s reasoning to a single dimension which consequently reduced creativity. The misconception survives a good portion of the 20th century until the 1990s when historiographical was introduced into the discipline.

Historiographical describes the inter-relation between mathematics, sociology and philosophy. It would be expected that mathematical concepts would be factual because it is a science i.e. with some form of explanations that can be backed up by factual experimental evidence; although the assumption is valid, not all elements in mathematics can be explained by the use of figures. For example, the establishment of a mathematical problem in the real life situation; that is to say, mathematicians often involves sophisticated techniques and values in solving a problem. However, when the issue is applied in real context, it appears simple and someone might be mistaken to think it’s just a matter of observation. Other examples of historiographical include the correlation between mathematics and other subjects i.e. social and natural sciences, education, religion and art, scientific advancements as well sociology (Archibald & Siegmnd-Schltze, 2016).

In 1998, Historian, sociologists, mathematicians, philosophers and ethonomasticians colluded with an objective to eliminate the long-lived belief that separated mathematics from other subjects. The representatives of each discipline made their contributions that disregarded the baseless belief that had been ingrained in people’s minds over several centuries. For instance, Historians who attended the 1998 conference,

Joan Richards and Henk Bos used various case studies to illustrate the need to change our mentalities concerning the interrelation of multiple disciplines. Joan Richards in her essay “of God and Logic and the Limits of Rational Man” demonstrates that it was necessary for mathematicians to ditch the old models that had been used before that decade for newer models. Mathematical models can be described as the representation of a theoretical situation into a figure that can allow one to visualize various features that could not be directly observed from a theoretical viewpoint. Past models were based on the religious principles where any notion that did not comply with Christianity were deemed unauthentic (What Is Mathematical Modelling). The use of religion as a standard limited creativity because people could only examine an issue from a single angle. Henk Bos supported Joan Richards as he used various case studies that revealed the roles of philosophical and sociological beliefs in Mathematic.

Sociologists, Mathematicians, and philosophers in the 1998 conference engaged in debate concerning the notion of proof which can be considered the primary feature of Sciences. For example, if we look at computer science that deals with the manipulation of various formulas to produce programs, mathematicians often believe that each step of the calculations can be approved. However, social scientists explain that the nature of the techniques used to solve a particular problem do not give logical explanations that are I line with mathematical principles. Additionally Edwin Abbot’s theory of multiple dimensions of any issue implies that we cannot explain everything as people tend to perceive things differently. The observation can be supported by the fact that mathematical

formulas involve theoretical principles or techniques that are derived from previous methodologies and thus do not use the standard inferences; this makes the rational explanation of the outcome impossible. As much as social scientists have a strong argument concerning the lack of prof in mathematics, mathematicians such as Arthur Jaffle point out that today’s math has expounded to a point where its complexities cannot be represented in a stepwise manner on paper. All the parties agree that mathematical solutions have some level of truth, but they also require some assumptions in explaining certain notions.
Other than the matter of the role of social sciences in mathematics, it is also important to examine the trends of the subject’s advances in the 21st century. From the history, one can learn that Mathematics originated in Europe and latter diffused into Islamic nations who contributed to its developments. In the 21st century, most people are embracing the fact that mathematics form the core of innovations; this has made the subject attractive. Consequently, the multiple interpretations of mathematics have increased creativity into the field; this, in turn, has made the study of the topic much easy as people are using devises such as calculators and computers in resolving mathematical problems (McKay & Lucia, 2002).

Conclusion

As we can see, mathematics cannot be considered a discrete topic as it has strong connections with other disciplines. The correlation has been responsible for many breakthroughs that have transformed our society. Given the trends that we have observed over the years, we can agree that the misconception that the community had believed in for centuries significantly slowed the rate of developments. However, the future is more promising

as people from different cultures are embracing mathematics which would encourage new ideas that will aid new inventions and innovations.

References

1. Archibald, T., & Siegmnd-Schltze, R. (2016). A publication of the International Commission on the History of Mathematics of the Division of the History of Science of the International Union of the History and Philosophy of Science. Journals of Elsevier. Retrieved from http://www.journals.elsevier.com/historia-mathematica/
2. Cooke, R. L. (2012). The History of Mathematics: A Brief Course. John Wiley. Retrieved from https://books.google.co.ke/books?id=CFDaj0WUvM8C=the+history+of+mathematics=gbs_navlinks_s
3. Kjeldsen, T. H. (2014). History of Science in the society. Chicago Journals, 214-315.
   McKay, & Lucia. (2002). Mathematics, New Trends. Mathematics, New Trends. Retrieved from http://www.encyclopedia.com/doc/1G2-3407500188.html
4. O'Connor, J. J., & Robertson, E. F. (1997, February). An Overview of the History of Mathematics. Retrieved from http://www-groups.dcs.st-and.ac.uk/history/HistTopics/History_overview.html
5. What Is Mathematical Modelling. (n.d.). What Is Mathematical Modelling. pp. 1-12. Retrieved from http://www.sfu.ca/~vdabbagh/Chap1-modeling.pdf
6. Baron, M. E. (2014). The Origins of Infinitesimal Calculus. Elsevier. Retrieved from https://books.google.co.ke/books?id=OcTSBQAAQBAJ&dq=infinitesimal&source=gbs_navlinks_s