What do jokes tell us about mathematicians?

Every profession fosters an image of its practitioners and how they differ from those in other walks of life. Jokes contribute to this construction. The jokes practitioners tell about themselves often highlight aspects of the profession which its members think are important, perhaps by exaggerating the properties which define that profession, taking them to extremes so that an absurd conclusion results. These jokes are likely to be appreciated by members of the profession but may not be understood by others. They are part of the way in which a professional community defines itself and differentiates itself from outsiders. Some jokes are incomprehensible to outsiders - if you understand the joke, it proves that you are an insider!

Here are four old jokes which have been in common currency amongst academic mathematicians for many years. What do they tell us about being a professional mathematician?

Jokes about mathematicians which are perhaps more contemporary can be found at webcomics like the specifically mathematical "Math Comic" Spiked Math and the more general xkcd, "A webcomic of romance, sarcasm, math, and language." Here are two examples:

The Spiked Math comic is licensed under a Creative Commons License.
The xkcd comic is licensed under a Creative Commons Attribution-NonCommercial 2.5 License.

We are grateful to Professor Kevin Parrott for recording these jokes.