Long ago I took an oral exam Algebra and my professor asked me the following: "Let $G$ be an abelian group of order 17020. What is its commutator subgroup $G’$?" At first I focused on factoring the number, but in a few seconds I realized with a smile that he said abelian and of course gave the right answer. Afterwards, I found the question very funny.
On another occasion I sat down with another professor over lunch and we discussed group theory and suddenly he quick-wittedly remarked: can you classify all groups $G$ with only a single non-normal subgroup $H$? Of course, such an $H$ must be normal by definition and without saying anything we could not resist to roar with laughter …
Have you also come across some of these sorts of math jokes?

  • $\begingroup$ This is related to this and this MO thread which is pretty much an exhaustive list. $\endgroup$ – Eugene Jun 25 '12 at 22:24
  • $\begingroup$ Also see this AMS notice. $\endgroup$ – anon Jun 25 '12 at 22:33
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    $\begingroup$ Not a math joke, but if you google, you'll find a lot of otherwise smart people speaking very seriously about the difficulty of factoring primes. In fact, we just had that on a separate post here. But they weren't funny on purpose, so I guess it doesn't count. $\endgroup$ – Arturo Magidin Jun 26 '12 at 1:30
  • $\begingroup$ @Arturo Wow, that MSE comment 3 hours ago is already number 3 in Google matches for "factoring large primes". It is surprising how often that phrase appears, even in refereed publications, e.g. in CACM '89 "The recent reports of factoring large primes with a network of microcomputers suggest that this is a problem well-adapted to such a scheme". $\endgroup$ – Bill Dubuque Jun 26 '12 at 2:15
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    $\begingroup$ @BillDubuque: If I understand the way that Google displays results, the fact that you and I visit MSE often may affect how high it shows up in the search on our computers (assuming you keep some cookies associated to MSE). That is, my understanding is that the exact same search may result in different rankings depending on local information on the computer doing the search. I could be wrong, though.... $\endgroup$ – Arturo Magidin Jun 26 '12 at 3:48

I’m fond of the first exercise in the second edition of Edward Scheinerman’s Mathematics: A Discrete Introduction:

Simplify the following algebraic expression: $$(x-a)(x-b)(x-c)\dots(x-z)$$

  • $\begingroup$ I like this one, as well as the indignant response that sometimes follows about how the answer is 26 and you are just having some type issues with the variables. $\endgroup$ – Francis Adams Jun 26 '12 at 1:58
  • $\begingroup$ Why is it 26? ${}{}$ $\endgroup$ – MJD Jun 26 '12 at 3:52
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    $\begingroup$ It remainds me of that old joke: What is a product of all numbers from -33 to 41? $\endgroup$ – default locale Jun 26 '12 at 4:32

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