A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.
So you can relate dimensions to the physical world, but the way we tend to think of them in math and physics is more abstract. Generally I think describing them as “degrees of freedom” is accurate; they are extra ways of viewing the functions or concepts you’re working with. Higher dimensions allow us to discern information about the lower dimensions we exist in, much the same way higher order derivatives show us behavior of the lower level function. Dunno if this is helpful I might edit this in the morning when I’m not sleepy to make it more useful
So you can relate dimensions to the physical world, but the way we tend to think of them in math and physics is more abstract. Generally I think describing them as “degrees of freedom” is accurate; they are extra ways of viewing the functions or concepts you’re working with. Higher dimensions allow us to discern information about the lower dimensions we exist in, much the same way higher order derivatives show us behavior of the lower level function. Dunno if this is helpful I might edit this in the morning when I’m not sleepy to make it more useful