Suppose we have an intelligent alien who has landed on Earth and has somehow found his way into a human high school math class (for the sake of scenic stability, the alien has the ability to cloak itself as a human form).
The typical trope is the alien finds the human math elementary, and quietly chuckles to himself about how primitive humans are. Sometimes the alien, when interacting with his human friends, mutters advanced mathematical equations to himself, which goes right over the humans’ heads. In our high school math class, the alien gets called up to the board and sometimes inadvertently fills up the entire blackboard to the shock of the human teacher.
For example, in the Animorphs series, there’s a line where Ax (an alien posing as a human teen) says in a train of thought:
I think I remember the equations ... in an equation where t is time, z is Zero-space, w inversely cubed represents the nexus of…
But how realistic is it that an alien would have the same concept of algebra as we do? Would our equations even make sense to them? Would theirs make sense to us? Would they even have “equations”? Would they have the concept of things like a variable or a square root? Would things like “subtract x from both sides” make sense to them?
Note that I’m not asking about symbols—we assume that, just as our friendly space alien has learned the English alphabet, he also knows about human symbols such as
+ – = × / √, etc. He also speaks the English language well (or has a translator chip in his brain). I’m also not asking if the alien would have problems with arbitrary conventions in our mathematical system (i.e. base 10, 360° in a circle, etc), rather the underlying system of logic. I’m asking that, if our mathematical glyphs were intelligible to our alien, would he feel right at home performing algebraic operations on Earth? If our alien came from a planet with a completely foreign algebraic system, how quickly could he pick up “human” algebra? How much of his native algebra knowledge could be transferred to his new context?