Heuristics Lead to Rigour

As you learn more ideas in mathematics, it’s easy to start feeling like certain ideas are “below” you. This often comes in the form of saying that ideas are “trivial”, as if they shouldn’t take up any of your time. This can be exacerbated further in mathematics by the idea of rigour. Once we learn that not all proofs are equal, it can be tempting to say, “Okay, I get this proof, but that’s not…

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Knowledge From Repetition

When I’m sitting in class and listening to the professor, I get frustrated when they go over a concept once and then continue on as if everything is clear. I think to myself, “Do they really expect us to understand a concept from just one example?” And yet, I realize that I do the same thing when I’m working with a student. This is a bit disconcerting, and it reminds me that teaching is a…

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I Could Be Wrong

As a physics student, I’m taught over and over again that science is about checking to see where we have made incorrect assumptions. The goal of science is to correct our assumptions about the world, and find better descriptions for what is going on. Of course, this is a distilled version of the goal of science (and I imagine some would disagree), but my point is that science aims to perform a consistency check on…

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