Mathematics
More Than Just Numbers
Understanding the essence, mindset, and the beauty of the order in God's creation.
The Essence of Mathematics
The first thing that typically comes to mind when people hear the word 'mathematics' is numbers and calculations. It is true that the mathematics we study from elementary school onward is largely dominated by topics related to numbers and arithmetic. However, these three elements are not mathematics itself; rather, they are merely one manifestation of it.
Mathematics is the study of rules—of any kind. These rules may arise from human creation (such as games) or from human observation of real-world phenomena (such as economic patterns). Because the world is orderly and such order is found everywhere, the scope of mathematical study encompasses all things.
The rules studied in mathematics are not arbitrary, but rather rules that are abstract, consistent, and combinable to produce specific consequences. In mathematics, these rules must be reducible to simpler ones. Mathematics deals with fundamental components that can be assembled into new constructs—much like a game of Lego.
Essential Elements in Mathematics Learning
Modeling
In the real world, there are various phenomena characterized by order—such as the motion of objects, music, and human relationships. When people seek to study these phenomena, they need a tool to discern the patterns within and temporarily set aside irrelevant elements. Mathematics serves as an appropriate tool for this purpose.
Deduction
At the heart of mathematics lies deduction. Deduction is the process of drawing conclusions in order to extract information that is not explicitly stated in the given premises. For example: “All XI grade students must participate in the study tour,” and “Joni is an XI grade student,” together imply that Joni must participate in the study tour — even though neither sentence states this explicitly.
Proof
Proof is a direct application of deduction. Mathematics contains a vast number of statements whose truth may not be immediately clear to those who hear them. For example, the statement “There are infinitely many prime numbers” may not be obviously true to everyone. One might even choose not to believe it.
Induction
Induction draws general rules based on patterns. A mathematician observes patterns and attempts to infer the underlying rules that generate those patterns. Many mathematical formulas originate from recognizing such patterns, which are then formalized into explicit formulas.
Problem Solving
Many real-world problems have definitive solutions. Some of these problems have already been modeled, allowing us to follow specific procedures to solve them. Others do not have standard procedures due to their complexity. Such problems are like puzzles—we have the pieces but do not know how to assemble the complete picture without trial and error.
Communication
The ability to think is important not only for the mind but also for the mouth and the hands. Often, we do not know how to communicate what we know. This is what distinguishes a seer, a practitioner, from a teacher. A seer does not know how they know. A practitioner knows many things but cannot explain them well. A teacher is required to know how they know and to be able to clearly explain what they know.
Mastery of concepts and procedures
As previously explained, some problems already have established procedures that can be followed. We need to teach general procedures for problem-solving so that students can apply them both for practical purposes and for mastering more advanced knowledge.
“Learning mathematics is not merely about memorizing formulas,
But it is about developing a way of thinking.”
Mathematics education must equip students with the thinking skills they need to live in society and fulfill their calling. One day, they will engage in important tasks, create impactful works, and make meaningful contributions to the world. Some of them might say, "Learning mathematics was useless; today, I do not remember a single formula I studied," while unknowingly applying a solid foundation of thinking skills. Although this may seem contradictory, it is not entirely incorrect. Most of the formulas they once learned will be forgotten, just as a programmer does not remember every instruction used in their code. However, what truly matters is the development of sound thinking skills — that is what will distinguish them from those who have not studied mathematics.
Mathematics in the Perspective of the Christian Worldview
The foundation of order is consistency that originates from within God Himself.
The foundation of order is consistency that originates from within God Himself. God cannot contradict Himself (2 Timothy 2:13, Hebrews 6:18). Mathematics is not only the study of consistent facts but also the study of the consequences that can be derived by combining a set of facts. For a Christian mathematician, our God is a mathematical God.
God created an orderly universe. Just as an artist can be known through their works, the mathematical God can also be known through His creation. We can observe order in everything, from galaxies to atoms. Trees, rivers, animals, and humans all exhibit order in their growth and interactions. Beautiful geometric shapes abound in nature: from the nautilus shell, honeycombs, to the fractal patterns of trees and lightning.
"When we encounter such phenomena during the process of learning mathematics, we are able to pause, admire, and reflect on the meaning of the existence of all things. Ultimately, these beauties lead us to gratitude and to delight in God through aspects that cannot be experienced through anything else."