absent
Explanation
The Joke
A student asks a professor why he is so absent-minded, and the professor says he will consider three cases. In Case One, he asks: when you fail to solve a math problem because you were distracted, do you wear pants? The student says yes. In Case Two: when you fail to solve a problem because you forgot whether you were wearing pants, do you wear pants? The student says "most of the time, I would think." In Case Three: every time you forget how brilliant you are, do you ever wear pants? The student responds "By God, no, never." The professor declares "Q.E.D." -- as if he has just completed a formal mathematical proof.
The comic parodies the style of mathematical proofs (specifically proof by cases) by applying rigorous logical structure to a completely absurd question about absent-mindedness and pants-wearing. The "proof" demonstrates nothing coherent, but it is presented with the confident formalism of a legitimate theorem.
The Humor
The joke operates by contrasting the meticulous logical framework of a mathematical proof with utterly nonsensical content. The professor uses "consider three cases" and "Q.E.D." -- hallmarks of formal reasoning -- to arrive at a conclusion that explains nothing about absent-mindedness but instead reveals that he is so absent-minded he has constructed an elaborate non-sequitur about pants. The student's gradually decreasing confidence in whether they wear pants adds to the absurdity, as the professor's bizarre line of questioning somehow becomes persuasive within the scene. It is a meta-joke: the proof itself is an act of absent-mindedness, which is the real answer to the student's original question.