Skip to Main Content

Adam-Graham-SquireMathematics in My Liberal Arts Education: Shaping My Past, Present, and Future

By: Adam Graham-Squire, Ph.D., Assistant Professor of Mathematics

During my entire college career, I never took a single course on parenting, voting, or taxes. Without doubt, though, these are important topics many people must deal with in their lives. Parenthood: the prerequisites are quite a low bar, and do nothing to prepare you for the extensive challenges you will face in the first few years. Taxes: they only come around once a year, but when they do, they certainly make an impression. Voting: it is the bedrock of our democracy and an important way to exercise our power, but how do we determine which candidates have our best interests at heart? None of my college courses touched upon these topics. Despite this, today my approach to grappling with these kinds of challenges stems from my training in the liberal arts. My liberal arts education developed my habits of thinking and methods of reasoning which I apply to nearly every area of my life, my sense of humor included.

Many arguments exist for the benefits of a liberal arts education. A liberal arts education enriches an individual by introducing people to varied forms of beauty, literature and the arts. It educates our citizenry with a broad base of knowledge from many disciplines. In my opinion, though, the biggest benefit of my liberal arts education was learning how to think critically in an interdisciplinary way. Though I have not used some of the things I learned in college, the ability to make sense of my world through rigorous contemplation has paid off for me time and again—and I learned it through liberal studies.

I studied mathematics in college; a challenging course about mathematical thinking is why I chose math as my major. I enjoyed learning the strict and rigorous methods for writing proofs. As a math major I also learned to take careful notice of definitions, to milk them for all of their meaning and then to use that information to construct solid arguments. I discovered it was not enough simply to have good reasoning; the explanation must also be laid out in a manner understandable to others. I realized that although problems are often unclear at first, with careful thought, effort and diligent parsing of language, I could eventually reach a solution. Lastly and perhaps most importantly, I discovered that none of those things were specific to mathematics. As I was enrolled at a liberal arts school and had many other interests, I took multiple courses in the classics, history, and religion. Woven throughout all of those courses was the theme of diligent scrutiny and evidence-based analysis. I came to realize that the habits of mind I developed through studying mathematics, that I thought were particular to mathematics, were in fact employed in many other liberal arts courses. In particular, I recall writing critical reasoning papers in English courses by asking myself these questions: Did I have evidence from the text to support what I would claim as facts? Did my conclusions follow logically from those facts? How could I arrange the arguments in a way that my solution would be easily understood? In history, I applied the same mathematical scrutiny to historical context and the bigger picture: what was it about particular situations that drove change? How could we predict the results of historical events? Can we apply our knowledge of those events to our current circumstances?


As I have grown older I have discovered that those methods of thinking, gleaned from different courses in college, apply not just to academics but also to living. My personality, my sense of humor, and my way of attacking an obstacle were all shaped by my liberal arts education. As a parent, I have faced a number of challenges I had no idea how to solve: children who will not sleep through the night, who will go through long stretches where every word is a scream or a whine, who have not had a bowel movement in a week. Each new parenting challenge brings an opportunity to investigate the root of the problem, research potential solutions, and then experiment to see which solution is most successful. I am able to make predictions and consider long-term consequences. Thanks to my education, all of these steps are natural means of examining my world around me. The variety of courses I took also gives me a breadth of topics to introduce to my children. Though I am not sure he fully grasped it, I know deep down my son appreciated learning why the ending to the LEGO™ movie was a quintessential example of the deus ex machina. Nietzsche would have been proud of my explanation, though perhaps a bit saddened at the continued death of tragedy; he would likely complain that everything is not awesome.

Everything is also not awesome during tax season. Each year tax rules change, and so each year my first step is to gather all my resources and materials. I go through line-by-line and complete the algorithmic steps laid out in the tax documentation. Taxes can be complicated, much like many of the courses I took as a student. As I learned from those courses, though, my taxes are more understandable when I break them into smaller pieces, and work through each piece at a time. Moreover, those courses taught me that just because something is complicated does not mean it is impossible. By following a logical thought process, I can demystify Schedule D from form 1040 in the same way I deciphered works by Sophocles and Euripides during college; all of the information is there, I just need the patience to find it, piece by piece.

With politics as well, I look through a lens that highlights both logical reasoning and hypocrisy. When trying to decide who receives my vote, I examine the arguments of each politician and ask the same questions my college professors asked of me as a student: Does this person recognize facts, build a logical argument around those facts, then follow where that reasoning leads them? Does this person make a particular argument in one situation and then make the opposite argument in another? The answers to these questions indicate which politicians consider the facts and will make decisions based on evidence to improve the lives of others, and which politicians are trying only to get elected.

Not only do these habits of thinking influence decisions I make on a daily basis, they have also become a defining factor in my humor. In my studies I used a technique called “proof by contradiction” to check for the validity of mathematical statements. This method begins with a statement one wishes to prove as true. The opposite of the statement is then assumed true, and the absurd conclusion, such as 0=1, that logically follows this assumption is the “proof by contradiction”. If the conclusion is false, and the logical reasoning is correct, then the assumption must be false—this serves to prove the validity of the original statement. The general term for such an argument is reductio ad absurdum, and I employ this style of argument humorously quite often, especially when parenting. One recent morning on the way into my daughter’s elementary school, she handed me her stuffed animal bunny. Having nowhere to put the bunny, I unbuttoned a few buttons on my dress shirt and stuffed the bunny into my shirt, half in and half out. As we walked into the cafeteria, some children told me I should not put the bunny in my shirt. In feigned astonishment, I asked them where it should go, since it did not fit in my pocket. As the debate raged on, other students came over to giggle at my questions and assertions that the bunny was real and not a stuffed animal. The same kind of absurdity I would use to disprove a mathematical statement served to indicate to the children that I was joking, not seriously claiming the stuffed animal bunny had magical powers, which would destroy me if I removed it from my shirt.

The liberal arts education I received did not just give me knowledge and critical thinking skills, it trained me in the way to think, to apply my methods of reasoning to other parts of my life. The habits of mind I gained have enriched my life by changing who I am, how I laugh, how I view the world, and how I approach obstacles. I hear many pundits say that college needs to prepare students for the workforce, which I find profoundly false. College needs to prepare students for the future workforce. I have been told that most of the jobs my students will hold 20 years from now do not yet exist. This makes it even more important that they not simply learn one discipline in isolation, but that they know how to think well in many areas, and how to apply that thinking to learn new things, to grow, and to excel in a future that is unknowable. In that sense, my experience demonstrates that a liberal arts education, and the vision of interconnectedness it engenders, is the best possible job and life training that humankind has ever devised.