On the Study of Quantitative Subjects

By ​Johnathan Li ‘24

One of the ways that we, as students, often describe our preference for academic subjects is by classifying certain subjects as more “mathy” than others. This particular label is often more fundamental than others, and it has always been of interest to me as to why, out of all other ways to differentiate academic fields, the math vs. non-math distinction is such a prevalent one; for example, “I am not a math person” is said more often than “I am not a geography person”, and it seems that the term ‘math’, here, is not merely the subject that shares the name, but the more general quantitative aspect of computation. This article seeks to defend the “quantitative subjects” from the inaccurate, though understandable, biases against it; this article also includes practices that have helped me through my academic journey and which, I hope, can also be of help for underformers going into challenging STEM courses.

The first thing to bear in mind is that portraying knowledge quantitatively, as opposed to qualitatively, is meant to simplify information. If a fact can truly be presented more efficiently by words, typically, unless for the sake of technicality, they are not written in quantitative language. Students often find mathematics challenging for good reason, since, at the end of the day, mathematics involves numerical and computational symbols that exceed day-to-day language. However, the fallacy lies when a student equates this difficulty with the notion that mathematics is inherently an excessively complicated way to present intuitive concepts. This cannot be further from the truth. Mathematics can feel confusing not because its presentation of concepts is convoluted, but because the things it seeks to present are themselves complicated; trying to present those things in a non-quantitative way would counter-productively complicate the information.
           
In the short term, however, mathematics does seem to complicate ideas; this is an unfortunate reality, especially for the lower math classes. Whether or not one considers this fact to be a blessing or a curse, quantitatively oriented subjects are unique in the sense that they have to be self-corresponding: there is no leeway for conflicting numerical results. The efforts of bridging subfields within these subjects, therefore, require axioms and definitions, which although can seem redundant, are crucial to verify the validity of theories. The advantage of mathematics as a self-referential language is that correct answers can always be verified through other means. Consistency between axioms automatically guarantees correspondence with truth; successfully applying one method of literary analysis, however, does not guarantee that it is the “right” way to understand the literature (though that is of its own beauty).
           
Quantifying things, therefore, allows us to see the subtle nuances in the data that were otherwise hidden. Applying numerical analyses offers a shortcut in dealing with highly sophisticated systems through a series of theoretical simplifications. This is especially important to understand how one ought to learn mathematics. If there is one takeaway from this entire article it is the fact that ‘understanding is more important than memorization’. Students often prefer to memorize how a certain question is solved in the textbook example rather than understanding the theoretical concept at hand. Truly understanding the ideas behind a field of study would make so many theorems and definitions, which students often chose to memorize, self-apparent. Without logical understanding, one cannot sustain mathematical development, and sooner or later numbers will appear completely detached from reality (calculus students can especially resonate with this sentiment, for accompanying every new unit there would always be a period of confusion as to “what derivatives mean in this context!?”). Understanding takes more effort in the short term, but it is crucial for achieving long-term success in mathematical reasoning.

As much as one might dust this entire article off by saying “I am not going to do ‘math’ in college,” the skill of breaching through the surface and getting to the theoretical roots of a particular topic is essential in the humanities as well: APUSH students have learned to respect the ‘big picture’. It is fine for one to recognize that they may find mathematics more difficult than others, for sometimes the method of reasoning in quantitative subjects just comes more naturally for some, yet it is unhealthy for one to use the ‘mathematical excuse’ to evade genuinely engaging with academic materials, regardless of the subject matter. For underformers going into their 5th form year, it is my suggestion not to give up on choosing a challenging quantitative course, for the benefit of both academic and personal development.