My theory professor on...
- Proof by contradiction: "I am going to say a wrong thing now! Don't listen."
- Injective functions: "If you have n things at the beginning and n things at the end, then everybody was busy getting something."
- The pigeonhole principle: "If you do not want to repeat yourself, make sure you do not speak more times than the number of things you know how to say."
- The pumping lemma: "The pumping theorem is sometimes called a 'lemma' for historical non-reasons."
- The use-vs.-mention distinction: "When you say 'My elephant is sick today', you mean that your elephant is sick today."
- Nondeterministic automata: "So, for this automaton, my medical report would say 'Schizophrenic patient; is in states three, eight, and eleven.'"
Also, his accent is such that I can't tell if he's saying "nesty" or "nasty", as in "We can make this expression as n(e|a)sty as we like." Luckily, it doesn't matter.