No, I don’t want to turn this into some sensational piece about declining school systems. Instead, I want to talk about a very real feeling that I experienced while studying this semester. First, let me set the scene. I’m a graduate student in theoretical physics. As this might suggest, I deal with mathematics on a daily basis. It’s just a part of the toolkit that makes me a scientist. It shouldn’t be much of a…

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When something doesn’t make sense, it’s easy to look at it and think that it is just a collection of random rules. Unfamiliar topics look incomprehensible, so naturally we miss the structure behind them. This doesn’t mean that the structure isn’t there. It’s simply that you can’t see it because you don’t understand the topic well enough. This happens all the time in mathematics. On the one hand, this is very odd. Mathematics is the…

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I am keenly aware that we live in a culture that likes things to be optimized. We are bombarded with messages of the finiteness of our time, which makes us seek activities that will give us the greatest return on our time. (Just that phrasing should set off alarm bells.) We aren’t supposed to “just” have hobbies. Our hobbies should boost the rest of our life in some way. Furthermore, we should engage in hobbies…

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If you’re like me, chances are you have felt like you aren’t doing enough. Maybe that means not studying enough in school, or perhaps it means not doing enough extra-curricular activities. Maybe you do have hobbies, but you feel like you need to do more. I’ve been there. If this is something you identify with, I would like to pose a simple question. Where did the idea of not doing enough comes from? Sure, you…

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There are points in our lives where we can feel that we are at a junction. Sometimes, we can only notice this after the fact, but there are instances in which it is clear. At those points, we are faced with a choice. Do we continue on, or do we retreat? In the abstract, we all know the answer. “Continue!” But that’s much easier said than done. Even if it is clear to everyone (particularly…

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Are you slow at what you do? This is a bit of a trick question. After all, what does “slow” even mean? The reality is that speed is relative. If you don’t have something to compare yourself too, it’s difficult to talk about speed. However, it’s equally easy to forget that speed is a relative quantity. In other words, we often declare things like, “I’m so slow!”, forgetting that this doesn’t mean anything in the…

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Have you ever tried to express a thought and found yourself at a loss for words? Have you ever had a crisp idea in your mind that seems so obvious to you, but when you actually tried to articulate it to someone, they came away with none of the clarity you had? If so, that’s a problem of communication. More specifically, it’s a consequence of being unable to organize your thoughts. This is a harsh…

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When trying to do something at a high level, it’s easy to feel like you need to approach everything with the utmost seriousness. After all, your pursuit is important! If you aren’t serious, then people will think you aren’t really into what you do. The drawback is that we can become caught up in our own sense of importance. We start to see our work as world-changing and critical for humanity. We then get upset…

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When I first began working as an undergraduate researcher, I found myself lost within the topic I was studying. Prior to the summer, I did not have any exposure to the area, which meant I had to climb the steep learning curve that blocked me from being able to contribute. It was frustrating. For a long a time, I wasn’t sure if I was even going to make it to the other side. I would…

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What can you do that no one else wants to do? What do you find yourself capable of doing, over and over again, even when everyone else has left or decided it isn’t fun anymore? In other words, what can you endure? These are questions that I think can help us clarify the activities that we should be pursuing. We all want to contribute in some way. The problem is finding the “right” thing. There…

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