The Relationship Between Mathematics & Physics
Understanding the relationship can eliminate much confusion.
In mathematics you are free to construct anything you like as long as it's consistent. So for example, in mathematics n-dimensional spaces really do exist. They are well defined mathematical objects.
Physics uses mathematical objects to model reality - with varying levels of success. The fact that physics may use a mathematical object to model reality does not mean that object now exists outside of mathematics. It doesn't. It simply means the object is useful in modeling reality.
So for example, do n-dimensional spaces "really" exist? The question is meaningless. They exist in mathematics, and they are useful in modeling reality. But to ask if they "really" exist is a meaningless question.
Heck, it's even conceivable that something other that mathematics will ultimately be better at modeling reality. Very unlikely, but conceivable.
Content written and posted by Ken Abbott firstname.lastname@example.org