One of the most difficult things to do in life is to focus. Maybe you’re different than me, but I have a lot of trouble sitting down and focusing on one task or idea. Instead, my mind buzzes with activity while my hands do another. I’m always switching between ideas, and it takes a lot of energy to focus on just one. On a more macro level, my trouble with focus manifests in the types…

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No matter how much advanced mathematics you study, the great thing is that you rarely have to accept anything as-is. If you come across a procedure, technique, or result and you wonder how in the world it works, you can always retrace your steps and get back to the foundational reasons as to why it works. If you keep on asking “why”, you will eventually get back to your starting axioms. In between that and…

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We like being recognized for the work we do. This is even more relevant now, with the idea of documenting everything you do. (If it isn’t documented, did it happen?) We don’t want to do work unless there is some reward attached. This is true for both the “regular” work we do as well as our side projects. Despite claiming to enjoy what we do, I have fundamental doubts about how many people would continue…

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This is a question that students encounter over and over throughout their education. It crops up when deciding what classes to take, what projects to embark on, and what programs to study. It is a natural question, because we don’t like embarrassing ourselves. Therefore, we want to avoid pursuits that are too difficult if possible. As a physics and mathematics student, I can only give you my perspective from this small corner of life. How…

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Learning mathematics is an additive process. What I mean by this is that new mathematics often builds on what came before. Learning mathematics isn’t exactly a linear journey, but it’s a good enough rough approximation. In order to go from one concept to the next, it’s useful to offer analogies to explain what is happening. For example, when you first learn to count, you learn about the natural numbers. These are positive integers that grow…

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