Familiar Forms

When you first start solving a problem in mathematics, the goal is often to find a way to express the problem as some sort of differential equation. During this initial search, you don’t care how the equation looks. It’s more important to get it written down so that you can proceed. However, once you do have an equation, the first step is not to try and solve it. That’s a rookie mistake. Instead, the question…

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Snapping Into Focus

Learning new ideas in mathematics or science isn’t always easy. Heck, I would venture to say that most of the time it’s difficult. I imagine the experience is the same whether or not you consider yourself to be “good” in a given subject. That’s because, on some level, we are all in the same situation when it comes to learning. We need to figure out how to integrate new knowledge into our existing worldview. In…

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Escaping the Path

There’s a lovely forest near my house. It’s a wonderful place that looks exceptional in the autumn, where the fallen leaves of the trees cover the path in a flurry of orange, red, and yellow. I love running there because it’s so peaceful. Imagine that I told you I would show you this forest. After hearing me wax poetic about it, you’re excited to see it. We get to the forest, and I show you…

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Jeremy Cote 2019-01-13 15:21:54

When making work that’s important to you, it’s tempting to focus on improving your best work. After all, when you think of your work, that’s what first comes to mind. (You don’t think about the mediocre work.) Therefore, it makes sense to focus on that. By definition, this should be scarce. It’s not that you decide to sometimes do great work. Rather, it’s a simple consequence of looking at many pieces. Some will jump out…

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