It was February 2022. I had just decided that I actually, genuinely, wanted to become a mathematician. To seal the deal and force myself to follow through on my dreams, I filled out the form to transfer from Software Engineering to Pure Math, and the rest was going to be history. That evening, I was telling a family friend about my decision, and I received a question I thought I had an answer for:

“So why a mathematician? Isn’t being a programmer much more useful and relevant?”

The answer I thought I had was along the lines of “I find math important and fun”. But I knew that couldn’t really be my answer. I found programming plenty important and fun. I told that family friend something half-assed, and tried to dismiss my unsatisfactory explanation as me struggling to verbalize my motivation.

But the question plagued me. Why do I do what I do? Since beginning university, as I have learned more math and approached something close to a real mathematician (in the limit), my life has transformed from something I hated every minute of, to something deeply fulfilling. Why?

The first answer I proposed to myself was *beauty*. This feels like it makes sense, as I certainly find intrinsic beauty in the act of doing mathematics! There’s nothing quite like carving out my own little niche of understanding within the universe, in my case by discovering cool facts about calculus on higher-dimensional shapes that I can be absolutely certain are *true*. Nevertheless, math’s beauty can only be half of my answer. There are lots of things I find beautiful and fulfilling, from writing fiction to the programming I left behind. Why is math the only thing I can live with myself doing?

I’ve finally figured out the other half of my answer.

Infinity is big. It’s really big. I know it sounds obvious, but infinity is so, so big. The more I think about it, the more I realize nobody — not you, not me, not anyone — understands infinity. Analysis as a field of math prides itself on trying to understand the infinitely big and infinitesimally small, but if you look closely at any analysis textbook, no matter how many times the authors write the symbol ∞, nothing is truly infinite. A sequence that diverges to infinity is just one that has arbitrarily large elements, *not *infinitely large. A sequence that converges gets arbitrarily close to its limit, *not *infinitely close. See the subtle distinction there? We never actually invoked infinity, we just approximated it with something finite. Humans are really good at that. We don’t think of infinity as *infinite*, we replace it in our minds with something much, much smaller: “really big”.

It’s important that we do this for our own sanity. We live finite lives in a finite world, and eventually, in a finite amount of time, the Earth will be gone and humans will no longer exist in a form recognizable to us, if they even exist at all. Everyone I have ever and will ever make an impact on will eventually fade away, as I become forgotten. The universe is a sequence converging to its end, and no matter how many of its terms I affect, I can only possibly change finitely many of them: I lose, infinity wins.

This nihilistic confrontation with infinity has stared me down over the years as I have gotten better at math and engaged with infinity again and again, especially as I have pursued my dreams of understanding calculus, the field of math that professes to understand *infinitesimally small change*. These encounters have left me convinced of this fundamental fact: in the battle versus infinity, my defeat is inevitable.

So why am I here? I insist on living and doing math, not just despite this inevitability, but *in spite* of it, as I live a life where I come face-to-face with it every day. Why do I do anything in the face of this impending doom?

Well, why does anyone? I’m not special. Humans love to tell stories of impossible odds. If what I wrote above is at all true, an immediate corollary is that we live in the face of impossible odds every single day. It’s not a coincidence this is reflected in the stories we tell ourselves: think about the hero’s journey and its variants present across cultures. As people, we love stories of us succeeding despite the inevitable, despite the impossibility of life itself. To persist in this crazy world, we need to bring a relentless human optimism to the world, that this is all *worth it*, despite overwhelming evidence to the contrary. This optimism is fundamentally what I love about people.

And to me, nothing characterizes this human optimism more than the pursuit of understanding. Despite its seemingly obvious impossibility, we try to understand the universe every single day. Philosophers philosophize and artists create, all in the pursuit of this beautiful but ultimately impossible goal. But its impossibility doesn’t make it not worth trying.

My opponent in pursuit of this beautiful collective effort is infinity. I *need* to understand infinity and how it changes. In this goal, I will fail; infinity always wins. There is always more to learn, more to understand, more to fascinate me every single day until I am gone from this world. But no matter its impossibility, I *will* understand what I can, or I’ll die trying.

It’s like I’m in an infinitely long boxing match with the universe. My arms will break and my legs will collapse in the end, as I eventually go down for the count. But the least I can do, for myself, and for everyone I hold so dearly, is to square up and understand everything I possibly can, and in doing so, I will punch infinity in the face.

I know I’m trying to do the impossible. But all I can do is try. In the end, isn’t that what being a person is about?