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No disrespect to "why was six afraid of seven," but "base 10" is the funniest math joke.
I have made the mistake of unironically writing the phrase "base 10" before, and I recently cringed and also laughed at an old post of mine that used the phrase “base 60” over and over again. I almost caught myself writing “base 8” the other day. In the unfortunately unfindable-on-YouTube words of Mitch Hedberg (who was talking about Ritz crackers, but it works for numeral bases too) if you write “base 60” or “base 8,” you have no faith in the product itself.
Every base is base 10. That’s the whole point of the positional numeral system! In the base ten system, the farthest right place is the ones place, the place one to the left is the tens place, one to the left of that is the hundreds (ten squared) place, and so on. In base two, the farthest right place is for ones, the next one to the left is for the twos, the one to the left of that is for fours (two squared), and so on. In base two, the number two is 10.
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That’s how bases work in general. In base sixteen, the number sixteen is 10. In base twenty, the number twenty is 10. In base sixty, the number sixty is 10. So “base 10” means absolutely nothing, and I find that hilarious.
On shows like Star Trek where some kind of universal translator is a given, I always wonder how the translation programs deal with the fact that every species of alien would probably refer to themselves and their planet with words that would most naturally translate to the English words “humans” or “people” and “Earth” or “world.” (I recognize this is definitely not the least believable thing about universal translators.) The way modern mathematicians have defined a positional numeral system means that if the base we are using is not already understood, there is no way to communicate it using digits.
Base 10 is a very funny joke, but in order to facilitate communication, I am hereby dedicating myself to the cause of always spelling out numbers when I need to explain what base I am using. The English language also has base ten built into the way we form numbers—sixty seven is six tens and seven, for example—but at least the written forms of numbers avoid ambiguity because there is no different way to speak or write numbers to communicate that they are in a base other than ten. (I almost typed 10. Gah!)
We are so used to 10 representing the number ten that we don’t even recognize “base 10” as a joke, but it is. To me, that is what makes it the funniest math joke.