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My motivation for this question is twofold: On one hand, I'm studying algebraic topology, where - at least in the book written by Hatcher - there is quite a lot of handwaving (e.g. maps are continous because it's obvious from the picture). On the other, I'm going to be a TA next term, where it might come in handy to have some examples of handwaving gone wrong.

I'd like to see two types of examples:

1) Tell me about typical handwaving-related mistakes which math undergraduates are prone to.

2) Are there examples of handwaving in more advanced math that was possibly published and only the peer-review process uncovered it? The longer it took for somebody to notice, the cooler I'd consider the example.

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Check this out

That link is to a math overflow thread that has roughly 200 responses and covers a range of topics. It lists some commonly believed - but ultimately false - ideas in mathematics.

For example, one of the things it discusses is a commonly-held belief in American schools (primary and secondary) that Pi is 22/7, and is therefore a rational number.

I imagine that one thread will provide hours of reading and consideration! Hope that helps a bit.

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  • $\begingroup$ Thanks, that seems to be a very nice list/thread. $\endgroup$ – Paul Aug 30 '14 at 17:46

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