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Title:Is Mathematical Beauty the Main Motivation for the Progress of Mathematics? Essay Example

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IS MATHEMATICAL BEAUTY THE MAIN MOTIVATION FOR THE PROGRESS OF MATHEMATICS? 8

Is Mathematical Beauty The Main Motivation For The Progress Of Mathematics?

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Is Mathematical Beauty The Main Motivation For The Progress Of Mathematics?

Introduction

Mathematics is a science that focuses on the study of numbers, space and change and the interrelationships amongst them. The study may be done in its pure form as in pure mathematics or in its applied forms such as physics. Mathematics is applied in almost every sphere of life from computing to surveying, construction to driving, flying to tailoring, financial to military. Analysing the progress of mathematics, it can be acknowledged that it has been motivated by the beauty of mathematics; the desire of great mathematicians to find out the interrelationship between the various elements. This was the driving force behind great mathematicians such as Archimedes, Pythagoras and Eisten. On the other hand, more elements apart from the beauty of mathematics are required for its progress. Such elements include chance such as the falling of apple to formulate the gravity rule and the overflowing of the bathtub to formulate the mass rule. The following essay will argue why the beauty of mathematics is the main motivation element in the progress of mathematics and also discuss situations where this beauty had to be complimented by other factors.

Definition

Mathematics is a science that studies the interrelationships between numbers, change and space. Mathematics is studied as a pure or applied science (Russell, 1903). In its pure state, mathematics is aims at developing theorems that define the interrelationships between the three elements defined above. In its applied state such as in physics, mechanics and chemistry, mathematics aims at applying the theorems developed in pure mathematics in real life applications. Just as other subjects of learning, mathematics has undergone progress over time. This is implicated in the various theorems and discoveries that have been developed progressively over time. These progresses have been motivated by the beauty of mathematics and other factors. The beauty of mathematics is the love of mathematics that drives discovery of new concepts in mathematics; hence contributing to its general progress (Russell, 1903). The great ways in which numbers space and change interact is the basic definition of the beauty of mathematics. An example of this interaction is in trigonometry where the way in which the three sides of a right angled triangle interact with each other according to a specific formula (Kadison, 2002). The relationships between the angles of a triangle are another phenomenon that defines the beauty of trigonometry. This essay will relate various fields of study in mathematics, its beauty and the progress made by renowned mathematicians.

Trigonometry

One of the areas of mathematics where the beauty of mathematics led to substantial progress is trigonometry. Trigonometry is the study of triangles and interrelationships between various angles and sides (Dolenc, 2010).). The finely erected pyramids in Egypt are an illustration of the use of trigonometry in ancient years. The progress of trigonometry as a concept in mathematics can be traced back to Egyptian, Babylonian and Greek mathematics. The beauty of mathematics is illustrated in the development of knowledge and concepts that was led by mathematics loving individuals. The first major progress made in trigonometry was done in the 2nd century BC when Hipparchus, an ancient Greek mathematician developed the first table of sines and cosines (Toomer, 1974). Heron, another Greek mathematician developed the Heron’s formula that tries to show the relationship between the sides of a triangle and its area.

Advances linking geometry and trigonometry were initially made by Eulear, one of the greatest mathematics of the ancient age His work involved triangles in circles where chords were used to draw interrelationships between the two (Birman & Nomizu, 1984). Pythagoras then developed the Pythagoras theorem that is extensively used in modern day trigonometry (Bell, 1945). His research was motivated by his eagerness to study more about trigonometry from what his predecessors. The theorem outlines that the length of the hypotenuse of a right angled triangle is the square root of the sum of squares of the other sides (Kadison, 2002).

From the above discussion, it can be acknowledged that the beauty of mathematics, which is the desire to find out more about the interrelationships between numbers, space and change were the main motivators to the progress made by the famous mathematicians in trigonometry. The beauty of trigonometry is based on the desire to know more about how the angles and sides of triangles interact with each other.

Calculus

Calculus is another prominent area of study in mathematics that has attracted the attention of scholars and professionals as well. It is defined as a discipline in mathematics that focuses on the study of functions, limits infinite series, derivatives and integrals integration (Dawkins, 2005). The beauty of mathematics in calculus is based on desire to know how functions behave under various situations. Analysing the history of calculus, it can be acknowledged that the progress made in this area of study was motivated by the beauty of mathematics. Calculus is broadly divided into two elements, derivation and integration (Iversen, 1996). Derivation is the breaking down of an element of problem to finite parts whilst integration is the grouping together of the elements that have undergone derivation (Iversen, 1996). For this reason, the beauty of calculus is seen during the integration and derivation. Calculus was initially used in astrology and other religious activities. This ascertains the fact that mathematics is applied in various spheres of life. Analysing the contribution of various mathematicians to the development of calculus, it is identified that much credit of the interrelations known in modern day calculus are attributed to the works of Sir Isaac Newton and Gottfried Leibniz who were British and German scientists respectively (Cajori, 1919). The studies by the two mathematicians was based on various situations; though their findings are equally important to the progress made in calculus. Isaac Newton focussed his study on calculus on the physical and real life situations in the environment (Stedall, 1985. His studies were specifically instrumental in astronomy and were extensively used in the analysis of orbits. Isaac Newton’s works were instrumental in the discovery of the reverse interrelationship between derivatives and integrals. On the other hand Gottfried Leibniz’s works with calculus were focussed on graph analysis (Burton, 1985). Gottfried Leibniz is credited for coming up with the most of the notations used in calculus. In his works, he discovered the need for the use of standard notations in calculus operations.

From the arguments above, it can be acknowledged that the progress made in calculus was motivated by the desire to know more about how functions behaved when subjected to various situations. This was the motivating factor that drove Isaac Newton and Gottfried Leibniz to contribute to the progress of calculus, and ultimately mathematics.

Although the beauty of mathematics is the main motivation factor for the progress in mathematics, it can be argued that there are times when it chance is the motivator. The doctrine of chance also plays a major role, although not equally important in the progresses made (Simonton, 2004). Upon evaluating some of the greatest milestones made in mathematics, one cannot help but appreciate the contribution of chance in the progress of mathematics (Berlinski, 2000). The Newton’s law of gravity is one of the mathematical progresses in the study of motion that benefited from chance. It was by chance that Sir Isaac Newton was lying under a tree and an apple fell on his head (Verlinde, 2011). This is due to the fact that Sir Isaac had not designed to have the apple experiment to support his research. The natural phenomenon shed a lot of light on what Isaac’s research and led to the development of law of gravity. The Archimedes principle also benefited a lot from chance (Shankar, 2006). In a bathroom scenario that led to the famous ‘Eureka ! Eureka !’ utterances, Archimedes was able to prove the relation between mass and weight. Same as with the law of gravity, Archimedes had not purposed to conduct his experiment in the bathroom but pure chance met his study.

Although chance plays a big role in the progress of mathematics, it is important to note that in all discoveries that were supported by it, chance only came to confirm a study that was in progress. This justifies why the beauty of mathematics remains to be the main motivation factor for the progress of mathematics. Chance only compliments beauty.

Conclusion

Concluding, this essay has given an in depth discussion on how the beauty of mathematics has motivated the progress of mathematics. The essay discussed about how interests in trigonometry led to the progress of the prominent area of study in mathematics. It was argued that studies in trigonometry could be traced back to Egyptian, Babylonian and Greek mathematics. The essay argued that the desire to know more about trigonometry motivated mathematicians to study more, leading to the development of the table of sines, Heron’s formula and the Pythagoras theorem, that were all concepts that led to progresses in trigonometry. Analysing calculus, it was concluded that Isaac Newton’s interest in the field of mathematics led to the discovery of the reverse relationship between integration and derivation while Gottfried Leibniz’s works led to the development of notations used in calculus. On the other hand, it was also argued that chance also plays a major role in the progress of mathematics. On analysing the Archimedes principle and the Newton’s law of gravity, it was appreciated that the doctrine of chance has also contributed to the progress of mathematics. However, it was noted that chance only happens to those who have interest in the phenomenon related to it. From the arguments made in the essay, it can be concluded that the beauty of mathematics is the motivation behind the progress made in this field of study.

References

Bell, T. (1945). The development of mathematics. Courier Dover Publications.

Berlinski, D. (2000). Newton’s gift: how Sir Isaac Newton unlocked the system of the world. Simon and Schuster. p. 65

Birman, S., & Nomizu, K. (1984). Trigonometry in Lorentzian geometry.American Mathematical Monthly, 543-549.

Berlinski, D. (2000). Newton’s gift: how Sir Isaac Newton unlocked the system of the world. Simon and Schuster.

Cajori, F. (1919). Who Was the First Inventor of the Calculus?.

Dawkins, P., (2005).Common Derivatives and Integrals, Retrieved on 17th July 2014 from http://tutorial.math.lamar.edu/pdf/Common_Derivatives_Integrals_Reduced.pdf

Bressoud, D. (2010). Trigonometry,;1-18

Iversen, G., (1996). Calculus. Thousand Oaks, CA: SAGE Publications, Inc. doi: http://dx.doi.org.ezproxy.apollolibrary.com/10.4135/9781412983556

Kadison, R., (2002). The Pythagorean Theorem: I. The finite case, Proceedings of the National Academy of Sciences of the United States of America, 99(7); 4178-4184

Russell, B. (1903). The principles of mathematics. 1(1); 173

Simonton, K. (2004). Creativity in science: Chance, logic, genius, and zeitgeist. Cambridge University Press.

Shankar, N., (2006). Archimedes, Resonance, 11(10);3-5

Stedall, J., (1985). The history of mathematics: A Very Short Introduction, Oxford University Press, New York

Toomer, J. (1974). The chord table of Hipparchus and the early history of Greek trigonometry. Centaurus, 18(1), 6-28.

Verlinde, E. (2011). On the Origin of Gravity and the Laws of Newton. Journal of High Energy Physics, (4), 1-27.