Students at Christendom are equipped for a life of leadership and excellence after their four years at the college, gaining the same liberal arts education received by the saints, scholars, and heroes of the past two-thousand years. Integral to that intellectual formation in the time-tested liberal arts tradition is the study of mathematics — a major recently re-introduced at Christendom that has drawn numerous incoming students to the college.
For vice president of academic affairs Dr. Greg Townsend, the subject of mathematics is key to a proper liberal arts education, necessary to study for its own sake and for the benefits it brings to the intellect of a student.
Here is his reasoning why:
“Mathematics arises from a consideration of the quantitative aspects of real things, so its study is necessary if we are to fully understand reality. One cannot truly grasp the reality of something if we do not include its quantitative aspects: the number of lines in a poem, the height of a building, and the mass of a planet are just as important to understanding the nature of these things as the tone of the poem or the purpose of a building or the habitability of the planet.
Fr. William Wallace, in The Modeling of Nature, notes that in the case of inanimate matter, these quantitative aspects are so intrinsic to being that we can use mathematics to describe their very natures – as is done in chemistry and physics.
Mathematics has also been valued for its ability to train a student’s mind in the art of deductive reasoning. In the language of Aristotle and the Scholastics, mathematics deals with abstract quantity; a thing which is abstracted from the quantitative aspect of real things. Because of these closeness to actual things, its conclusions tend to be particularly easy for the mind to grasp. Thus, even a two-year old grasps that two is bigger than one—they always choose two cookies over one cookie—and that a straight line is the shortest distance between two points—the fastest way to get to Mom’s loving embrace.
So mathematics is the unique subject where a student can construct a logical argument and he or she has a sense of the validity or falsehood of the conclusion. Within mathematics, then, it is possible to study the logical structure of an argument, rather than the conclusions of the argument: does one statement truly flow from the other or is something hidden being assumed? In this way, a student can be trained in deductive reasoning. It was the Greeks who first developed this aspect of mathematics, and its earliest expression in Euclid’s Elements is still studied today.
Mathematics is also present in the liberal arts curriculum because it provides a foundation for the concepts used in the more abstract sciences like philosophy and theology. The concepts used in these disciplines are developed using analogies from the natural sciences and mathematics. In his work, The Way toward Wisdom, Fr. Benedict Ashley notes that Aristotle’s works are filled with references to results in mathematics in order to illustrate concepts he is discussing. Such concepts as unity, truth, beauty and causality arise naturally in mathematics and an understanding of them are necessary for mastery of philosophy and theology
Perhaps the most surprising aspect of mathematics is its beauty. It is a subject that deals with absolute truth – even the most ardent atheist accepts that ‘one plus one equals two’ – and our minds delight in the truth. Students of Euclid’s Elements, which deal with the geometry or the abstraction of our immediate sense experience, experience a delight as they master each of the Theorems. They ‘see’ the truth of the theorem in that they not only know the truth of it but also can perceive why it must be so. This experience gives us a little foretaste of Heaven – our final end – where we will ‘see’ Absolute Truth Himself.
From its beginning, Christendom College has been committed to a Catholic liberal arts education. The 86-hour curriculum is carefully designed to provide an orderly sequential presentation of the fundamental principles of mathematics and natural science, philosophy and theology in conjunction with the historical and literary knowledge that are needed to refine the human intellect. There is a great need for a student of mathematics to undergo this refining process. The concepts used in modern mathematics (post 1600’s) have gone beyond the concepts developed by the Greeks and reveal to us aspects of reality of which they were unaware.
Through the principles introduced in the core curriculum here at Christendom College, a student of mathematics will have a unique ability to carefully define the concepts used in modern mathematics. He or she will be able to understand the strengths and limitations of the modern concepts and identify the true source of these paradoxes. The student would be able to ‘carefully define them with a non-arbitrary reference to real quantity,’ to use Fr. Ashley’s phrase.”
To find out more about Christendom’s core curriculum, and about the challenging mathematics major, please visit christendom.edu/academics.
This story is taken from the spring edition of Instaurare, Christendom College’s quarterly magazine. To read more or subscribe, please visit christendom.edu/news/instaurare-magazine/