A research paper I wrote on the applicability of mathematics in other studies.
Mathematics in the Humanities
One of the great lies that is perpetuated throughout secondary education is that the study of mathematics is necessary only for a select number of people, and thus should not be a requirement for every student. While this is not something that is taught in school, and is considered a form of heresy by many high-school math teachers, this belief is still spread through the majority of the student body in an average high school. The main purpose for this lie is most likely to excuse the lack of motivation and poor work ethic a student may feel in his math course, so as to keep him from being held responsible for poor grades. Although the excuse may at first glance seem valid and reasonable, it is built on ignorance towards the true nature of mathematical studies.
Mathematics is a very abstract study that can include a broad variety of topics. It often involves formal systems, such as numbers or measurements, and seeks to formulate conjectures using these systems. Being able to work with these systems is a skill that is very important to every student, though it may not seem so at first glance. Unfortunately, the wide applicability of mathematics has of recently been largely ignored. The main reason for this is that people nowadays do not realize the broad spectrum of topics included in mathematics, nor do they understand how these topics are being used every day. Despite the assumptions of the modern layman, mathematical thought is a vital part of everyday life, and nowhere is this more evident than in the branch of studies known as the humanities.
The humanities are branches of knowledge that employ a critical and analytic outlook in order to study human culture and development. While it is true that the two fields of humanities and mathematics do employ different methodologies to study two very different things, it is also true that all throughout human culture (which is the focus of the humanities), humans have placed a great deal of importance in math. The end result of this is that in order to properly study the humanities, a good background in many different mathematical concepts is vital. Even more vital than this though, is the ability to use the logical reasoning that is essential to mathematical thought. Three branches of the humanities that demonstrate this best are philosophy, religion, and art.
When one hears the word “philosophy,” it is usually accompanied by images of Ancient Greece, which has been described, rightfully so, as the birthplace of Western culture, especially Western philosophy. In fact, our word philosophy comes from the Greek word meaning, “love of wisdom.” This is, thus, a very fitting word, as philosophy is, in essence, the study of thoughts and beliefs, in an attempt to ascertain which thoughts and beliefs are most wise (Kenneson). To this end, an invaluable tool for any philosopher is logic, which is reasoning that only accepts conclusions which are inescapable (Smith 83). This reasoning can be used to argue by making a few statements that appear to be self-evident, then making a conclusion based on these statements (Kline 26). The classic example is “if A=B and B=C, then A=C.” This logical reasoning is the basis of all mathematics. Thus, it is clear that mathematics play a vital part in all branches of philosophy.
Not only that, but one very important argument for the teaching of mathematics to students is made. If all mathematical concepts use this method of reasoning, then it stands to reason that an extensive study of mathematical concepts, as well as constant use of mathematical skills, will greatly benefit one’s ability to reason logically. Essentially, the more one studies mathematics, the more one is able to use logic and reason in his thinking.
The second branch of the humanities mentioned was religion. Of course, few people would typically associate religion with mathematics, or any sort of rational thought, due to the sheer amount of faith most religious beliefs require. It is true that much of religion, especially the Christian religion, is in many ways irrational, however, it was not always viewed as such. In fact, there was a popular school of thought in the Middle Ages that sought to seek rational answers for questions related to Christian doctrine, known as scholasticism (Sherman 248). The scholastic thinkers would pose questions to themselves relating to Christian doctrine (much as the Greek philosopher Socrates would) and try to find a rational, logical answer to them.
Again, while on the surface this may not seem entirely mathematical, the style of reasoning that scholasticism required was the same as that which is used in all forms of mathematics. Of course, the scholastic thinkers approached it in a more dialectic style, in which they would pose questions from every side of the issue, but these questions were all guided by a basic mathematic logic (Sherman 248).
Of course, not all mathematical activity the medieval thinkers took part in was wholly “logical.” Many theologians, despite possessing an unquenchable hatred for anything considered a form of sorcery or paganism, had a certain love for numerology, and often attached a certain divine meaning to numbers. The lack of logic in such an activity would cause one to not consider this a form of true mathematics, and while this may be true, it would also be incorrect to completely divorce numerology from mathematics. After all, many of the numerological theories of the Middle Ages were based off of a blend of mathematical and theological concepts. For example, due to the belief in the Holy Trinity, the number three symbolized the spirit, while four symbolized matter, because at the time the universe was said to be composed of the four elements of fire, air, earth, and water (Fleming 211). The human being was symbolized by seven, because seven is the sum of four and three, and the human being was believed to have been made up of spirit and body (Fleming).
The last branch of the humanities is art, which is probably the best example of the applicability of math into the humanities. This is because much of art, especially in antiquity, is based around measurements and proportions, as well as the relationships between numbers. Greek art is probably one of the best examples of this. The philosopher Plato believed that the universe was built according to geometric principles, and so it was important that human architecture and sculpture be the same (Fleming 58). For example, one of the quintessential works of Greek architecture is the Parthenon of Athens, which was originally built as a temple to the goddess Athena. Athena was the patron of wisdom and mathematics, so it followed that a temple dedicated to her should be built using proportions, and thus all measurements of the Parthenon follow a ratio of 9:4 (Fleming 30). It is not known what the significance of the 9:4 ratio was. It could have been that the ratio was meant to be 2:1, but the builders did not have precise measuring tools. Whatever the reason, it is clear that the Greeks were very concerned about geometrical harmony and symmetry, and this concern is reflected in their art.
Mathematical thought is not just important in the visual arts, but they are also vital in music, especially music theory. It was the Greek mathematician Pythagoras who first discovered the mathematical relationships between intervals, which are the distances between notes (Fleming 51). He also pointed out how this could be examined with a string that was stretched tightly enough to make a musical note when plucked. If the string is stopped off in the middle, the note that the string produces will be exactly one octave, or eight notes, above the note it would play if it were not stopped (Fleming). Thus, the musical octave is based on a ratio of 1:2, because the higher end of an octave is played on a string half as big as the string that would play the lower end of the octave. It is clear, then, that mathematical thought is built into musical theory.
Now, the question that remains is “why does this make mathematics applicable to the students who are being forced to learn it?” Well, as has been mentioned before, the study of mathematics does more than just teach students a bunch of random concepts about working with numbers, but it also helps them develop their logical thinking skills. In the modern era of science and technology, it is vital to be able to use logic in one’s thinking, and though the uses of logic have been revealed using older branches of knowledge, they are still applicable to a wide variety of studies besides math. Thus, the study of math is beneficial to many academic disciplines, from science, to philosophy, to medicine, and beyond. Not only that, but it is clear, through the example of the use of geometric proportions in art, that mathematical concepts are used in some way in nearly every study imaginable. Whether you’re trying to determine the best way to shoot a basketball, or the right proportion of ingredients in a cake, mathematical reason and knowledge is essential, and that is why it should be taught to all students.