Being a fan of mathematical logic and deduction, I found the following math joke to be elegant, punny, and utterly hilarious.


For those who don't speak math, an explanation follows.

'∀' and '∃' are what mathematicians call quantifiers in logic: the former is the universal quantifier, and the latter is the existential quantifier. They're usually followed by the variable they quantify, and then the expression in which they quantify it, and are basically used in logical theorems to denote how certain variables should be treated.

Much like in lambda calculus, and any other field that requires rigorous treatment of unknowns such as variables, variables can exist as either free or bound. A free variable is one to which no actions or values have yet been prescribed to, while a bound variable is bound by a quantifier. When a variable is universally quantified, this means that the statement in which it exist should be treated as if any possible legal value for the bound variable would be true. Likewise, an existential quantification on a variable means that there is at least one possible value for which the statement is true.

For example, the statement "∀x (∃y (x = 2 * y))" is saying that for all numbers x, there exists a number y such that twice y equals x. More meaningfully, it asserts that for every number, you can find half that number, a statement which is true over the real numbers.

The actual meaning of the joke relies on knowing that many statements in number theory end up quantifying two variables to manipulate, one with ∀ and one with ∃. Hence, the assertion that for all ∀ symbols, there exists a ∃ symbol nearby.