The mathematical connection of this famous routine is not obvious. But some important math concepts are at the root of this funny skit.
After you stop laughing and, if you are like me, wipe the tears so you can see straight, you may take a minute to think about why this is so funny. Clearly it is the use of ordinary words as proper names. But “who” and “what” are not just ordinary words. These are pronouns.
Considering the history of human languages, nouns, proper names and pronouns predate numbers, constants and variables by thousands of years. More importantly natural languages, like English and Chinese are much older than formal languages like the semantic aspect of mathematics. This is a very important point to keep in mind. For math, as a language, abhors ambiguities. Math cannot tolerate confusing numbers and variables. In mathematical terms proper nouns are numbers or constants and pronouns are are variables and in “Who’s On First?” Abbott and Costello do just that — they confuse numbers or constants with variables.
I include “Who’s On First?” in my math-humor collection because what makes it funny is the absurd exchange. And these absurds are rooted in ambiguities that we may tolerate in most normal communications. For a few moments we are made to see, if not to understand, the mathematical viewpoint of such ambiguities. This is an excellent illustration of the connection of strict mathematical concepts to ordinary language. If we remember this fact, we can often make those formal mathematical ideas much easier to understand.