On April 6, 2021, my father passed away. He rejoins my mother who passed away 20 years ago. The wound of losing my father is fresh, but I still wish to commemorate his life in my own way. We rarely discussed much, but there were few instances where we talked about math. My father was an electrical engineer, so he knew his way around numbers. He reminisced about how he didn’t learn calculus until his later college years; his mathematical knowledge ending at the Laplace transform in order to solve differential equations in electrical engineering.
Perhaps it’s inherited, but differential equations is the area I gravitate to the most. Maybe it’s the computation techniques that just stimulates my brain in a way that other fields of math have yet to accomplish. When I learned about DC and AC Circuits in my Physics class years ago, I thought about how this was the type of problems my father thinks about. I never talked to him about this, I mostly listened to him, sat in awe when he would configure the house’s electricity unit. How does he know exactly what setting to turn the knob to, what do those numbers mean to him, and how are they improving the quality of our life in this house? I never asked, I just stood back and watched.
The study of differential equations stems from the study of calculus (or analysis, if you want to be more technical). Differential Calculus was formalized with this notion of looking at how things change on a very small scale, on an epsilon-scale. How does this action change at the smallest interval of time? Or how different is the scenario between these two instances of time? Then, the added complexity of allowing these small changes to interact with one another is what births differential equations.
For example, the relationship between the speed of a ball that drops from somewhere, how high it was dropped, and how long it has been falling are bridged by differential equations. The change in speed holding hands with the change in height and the change in time. In a way, all differential equations are built on events and actions holding hands. If that’s too cheesy of an image, imagine instead that events sign a scientific contract that specifies if A affects B in one way, then B will affect A in another way. As an example, the contract between a car’s distance (A) moving at a constant speed signs a universal contract with the time that elapses (B). Here, the contract is Distance = Time x Speed.
Then with this analogy, the study of differential equations are mathematicians trying to peek into what that contract says, what does the fine print say about the agreements between Events A, B, C, and so on.
This seems broad, and it is. Differential equations appear in physics (fluid dynamics, heat diffusion), biology (diffusion of medicine), climatology (weather predictions), and even in economics (stock market predictions) and finance (compounding interest). Any phenomena occurring between two or more agents have some differential equation governing how they’re related. It’s an amazing subject! (Maybe I am a little biased.)
This is the subject that drove me to pursue a PhD. My desire was never to peek into the contracts of the universe. My desire was to teach and explain the beauty in mathematics and more precisely the vast stretch of land that differential equations touch. I thought that maybe I could inspire a generation of students to view math in the same rose-colored lenses that I glued onto my eyes.
I regret to say though that I never had the chance to share this deep, motivating desire with my dad. He never asked, just like I never asked. He was happy knowing that I was happy. My dad was a weird parent, he didn’t care about what my siblings and I did. Sure, he wasn’t always like that, but something shifted. He started letting us pursue and do whatever it is we wanted, so long as it made us happy. I even joked with him about doing drugs or drinking while underaged, and he laughed along and said “Alright”. It was weird. (Side note: I have never done drugs and only drink on special occassions.)
The one condition was that we had to get a college degree. This long-standing immigrant belief that a degree will open so many doors and opportunities for their children and their children’s children. The physical degree perhaps may not be as door-opening as it was before, but the experience of college and what it has given me are what my father probably imagined a college degree would provide.
After I received my college degree, it was Mission Accomplished. From here on out, it was entirely happiness-driven. What makes me happy? What will be the driving force that gets me out of bed for the next few years? It was teaching. My father was supportive, as he always was, and cheered me on. I remember the day I got an acceptance letter for grad school, calling him in excitement and forgetting about the time difference between Los Angeles and Amman. Happiness isn’t constant. Things have happened, are happening, and will continue to happen against and in spite of this happiness-driven life. But my father raised a very stubborn and strong individual.
To tie everything together in my own quirky way, the differential equation governing my father and I’s relationship has always been taking turns watching each other from behind, never peeking too much into each other’s lives. He took care of me just as any good parent should and would. He gave me freedom when it mattered. It is this freedom that allows me to freely dip my toes into anything I want.
My father was a strong and good person. Yes, imperfect also, but so am I. His heart was in the right place most of the time, and I owe much of my successes and bravery to him. To close this essay and commemoration, I share with you an intimate conversation where my father let me peer into his side of life.
My flight back from Los Angeles to Oakland was delayed a lot. It was past midnight by the time I arrived at Oakland and my father had been waiting since the original flight schedule. I felt bad. However, this late night drive granted us an open highway with no traffic, it was a smooth silent drive. I don’t remember what started the conversation, but my dad told me the story of my mother’s death and the aftermath.
I was two when she passed away. I had no idea what was going on, but he told me this story with detail as if it is still so fresh in his mind, perhaps it was still recent to him. But what stuck with me through the years is the aftermath. He told me how he felt lost and disconnected from reality as he drove back from the hospital with four very young children. Suddenly, he realized that he had been ignoring the road. He got scared. If he had kept being disconnected from reality, then he thought an accident would have happened. He said that the only thing grounding him in reality was his children.
His philosophy in life shifted, seeing how my mother could suddenly pass away made him realize how fleeting his life could be. My dad thought that he needed to raise his children in such a way that if something bad happens to him that we’ll be able to live on our own. This came with its own issues and challenges, but overall in my opinion, he accomplished his mission. My dad was smart, hardworking, and passionate. He did any and all things he could do to provide for us and give us a fighting chance at life and success.
I could go on for paragraphs talking about how much he gave and sacrificed. But, I think I will finish this with final thought. His death is earth-shattering. I can't find the steps to move forward quite yet. It was early in my opinion, but at least, he’s resting now. A man who worked for his five children for over two decades is finally able to rest. I send my prayers, thoughts, and tears to him.
Thank you for taking the time to read this. If anything, this was just a public therapy session and a peek into my life. I study math, because it has beauty, creativity, and finesse. I teach math, because I believe I bring warmth to a subject infamous for being cold. And I write math, because it is analogous to my life in ways I never notice until it is in writing. Here is a picture of my father, my mother, and I at my 1st birthday.
Uploaded 2021 April 14. This is a part of a monthly project which you can read about here.