>Would they use matricesI'd imagine they do, given how matrix multiplication is just one abstractions step away from (concatanating) linear problems.
>quaternions?The question here is whether they'd put the same hard focus on quadratic forms. Which they probably do, with a similar line of thought than why I think linear problems will stay relevant.
>trigonometryWhat do you mean by this, though?
If you subtract projection and all that geometry stuff which is already seated elsewhere, what's left of trigonometry. For most kids today, it's the course making you comfortable with some special functions. Doesn't really have to be its own subject - especially for creatures that learn differently.
>Would they have set theory?If there's smart and have combinatorics and induction, I see no way around them asking about the collection of sub-collections and this leads to a bunch of set theoretical question. A more concise way to ask if their stuff would look different than ours is to ask whether they'd naturally come up with the total order that is the ordinals beyond the natural number and other common order types. Would they introduce the transcendental induction and jumps and limit ordinals like Cantor did?
>How would they do topology differently?I feel there's lots of way to do it and our classification schemes are loaded with historical accidents
>>11242863I get where you're coming from, but I think there's common denominators whatever the way they perceive things. E.g. I think the Church Turing thesis may hold well (computation/process is something universal) and then abstract rewriting systems capture the range of "logics". If we at least fix math to be symbol manipulation, then if even their logic is different, it's not something we couldn't also do
https://en.wikipedia.org/wiki/Abstract_rewriting_systemIf we're going to speculate, then a question would be whether "they" have a similar notion of self and identity and apartness than humans do
