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Mathematics: stupid and clever questions for people who understand

A few months ago we had two similarly named discussions on physics and biology which, in principle, could form part of a long series, limited only by our ingeniousness in thinking of pertinent fields. Their purposes were to give people an opportunity to air the questions regarding a field that most puzzled them, in the hope others would then answer them. I'm sure I'm far from the only one who found those discussions fascinating, but we never seemed to get a third one. I feel like mathematics is the logical next step, which is why I submitted this idea for a discussion.

I'd better clarify a few things first:

(1) The physics discussion was begun by someone who had some questions of her own. The biology discussion was more of a "let's each debunk this creationist list of arguments" piece. The discussion I'm proposing here will be different again. I don't really have any areas of mathematics that confuse me, and I'd rather not guess for others what they find confusing and what they don't. I know from personal experience of one man who found mathematics interesting if taxing that the main things that confused him were why the product of two negative numbers is positive and how to make sense of statements that refer to nothing, but I think I should step aside and let others say what it is they don't "get". If one or both of those issues do come up, I'll explain them as best I can, which is what i did for said man.

(2) I'm not abbreviating it either as maths (UK; me) or math (US) to allow an international spread; I know we have plenty of people here from both nations, not to mention others. In the comments, call it what you will.

(3) Does anyone know what fields future discussions could address? If I was trying to invent one based on a field where I'm relatively ignorant I'd probably choose economics, but that doesn't seem like a logical next step here to the same extent. Of course, this "what else?" issue's value in getting us to discussion 4 shouldn't stop the primary focus here being on mathematics.

With those points out the way, let's get started!


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