Knowledge and Its Applications

When I think about mathematics (or knowledge more generally) and its relation to everyday life, my mind frequently centers on Raphael's The School of Athens. I distinctly recall contemplating this image during my first semester at Princeton. At the time, I was really enjoying the intellectual rigor of my first math class and knew I wanted to eventually make that the focus of my studies. One decision remained, given that I had to declare my major before the end of the spring semester (if I chose an engineering degree). Should I pursue pure mathematics or (the rather unique major) Operations Research and Financial Engineering (ORFE)?

Having only taken classes in the Math Department up to that point, I felt as though I had a better understanding of what specializing in that subject would entail. And my understanding of that, combined with my positive experiences with the Department, appealed to me. Indeed, as I mentioned earlier, the idea of pursuing irrefutable logical truths (subject to axiomatic assumptions) felt noble and aesthetically satisfying in much the same way that I've been drawn to Plato's Realm of the Forms. Naturally, I'm not the first to note this parallel between mathematics and philosophy. In the Republic, Plato does so himself. And, even today, some scholars assert that most mathematicians are Platonists (at least to some extent). Likewise, I've appreciated the beauty in things that, once proven, are true forever and whose presence can be found in a variety of contexts one would never expect (e.g., complex numbers).

However, it's at this point that I considered the other principal subject of The School of Athens. While Plato points upward towards the Realm of the Forms, Aristotle redirects his attention back to "the real world." Similarly, I stopped to think about my ultimate goal for myself and how my education should align with that. I knew I wanted to combine my love for mathematics and technology with medicine to improve healthcare at scale, but I wasn't yet sure how I'd do that. Still, I figured the best way to discover that was to study something that was simultaneously quantitative and technologically fluent while also being broad in scope and potential applications. My premonition, despite not having taken any departmentals up to then, was that ORFE was exactly that.

I couldn't be happier with my decision. Although I hope to eventually take some pure math classes, I know ORFE, with the deep fundamental knowledge of probability, statistics, and optimization it's given me, has uniquely prepared me to address the various challenges facing the healthcare system. Furthermore, it has helped me better understand myself. I do enjoy mathematics for its own sake, but I've also realized that I'm most excited to see the theory realized in practice, whether that be in finance, healthcare, or otherwise. In other words, there is beauty in truth itself, yet even more so when its impact is visible in something of this world. Perhaps I'm an Aristotelean after all.