Mathematical dimensions don’t have to relate to physical ones. Mathematical dimensions mean that you have coordinates where changing one coordinate doesn’t effect another. So if you have a point (x,y) and you change the x coordinate that does not effect the y coordinate. and you can have vectors (coordinates) of infinitely many components. (a,b,c,d,e,f,g,h,….)
Physics usually only uses 3 or 4 dimensional vectors to separate the 3 or 4 dimensions that we perceive. But if you for example want to track a population of something or many different atoms, you could also just for fun assign a dimension (or more) to each of the samples in that population and do maths with that. So that every state of a population is mapped to a coordinate.
It’s no longer feasible to understand that when you want to translate that to the physical space of 3 dimensions but it’s able to be computed and might give you useful results.
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