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The Importance of Analogies in Mathematics
One of the tools you use to explain something in natural language is the analogy. It's extraordinarily useful in helping people understand something they're unfamiliar with. So that is a deep part of mathematics and the thing that's hard about it is at the undergraduate level there's a reason one reason why we don't do it so much. You have to sort of understand the language and the formalities before you then test this.