Handwaving gone wrong

Question

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.

Related: 'Obvious' theorems that are actually false. In particular, I mentioned there that Frege's reliance on a principle of unrestricted comprehension is famous, because it wasn't until shortly before the publication of the second volume of Grundgesetze der Arithmetik that Russell pointed out that this intuitively appealing and crucial principle was actually false. — MJD, Aug 22 '14 at 19:15
Also possibly useful: Examples of apparent patterns that eventually fail. Related: Statements with rare counter-examples — MJD, Aug 22 '14 at 19:21

score 4 · Answer 1 · edited Apr 13 '17 at 12:58

4

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.

edited Apr 13 '17 at 12:58

Community

1

answered Aug 30 '14 at 12:16

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1,708

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

Handwaving gone wrong

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