I'm sorry if this question is too vague or otherwise a stupid question.
Suppose the mathematicians in some alien civilisation similar to ours sculpted their Mathematics in three dimensions (or higher), rather than writing it in two, ceteris paribus. Would they have an advantage over us?
I suppose the notation would be more information-dense, meaning more nuanced ideas might be better captured than in our own myriad ways of writing Mathematics on paper. (It's fun to imagine what it might look like.)
Then again, I suppose that since the dimensions are orthogonal, such notation could be unwrapped (or "coordinatised") to become a left-to-right string like so many of us are used to. This relates to the mantra of, "if you can do it, you can do it in a Turing machine!". (I don't understand this fully, so maybe it's where the answer lies.)
How much of Mathematics is limited by our writing?
I started thinking about this when solving some problems in Semigroup Theory, where knowing your left from your right is extremely important. I thought, "what about up and down, back and forth?" - and pictured notation like a Dominoes game.