Penrose, 1.3:
What I mean by [Platonic] ‘existence’ is really just the objectivity of mathematical truth. Platonic existence, as I see it, refers to the existence of an objective external standard that is not dependent upon our individual opinions nor upon our particular culture.
He follows in an example of Fermat’s last theorem: was it not “true” before it was proved? I like Penrose’s approach here: it is a soft Platonism, accepting objectivity, which is pretty necessary to assign meaning to scientific explanations, but placing it in a different category of existence form physics things. Has he says:
[Mathematical forms] do not have spatial locations; nor do they exist in time. Objective mathematical notions must be thought of as timeless entities and are not to be regarded as being conjured into existence at the moment thet they were first humanely perceived.
This is a nice, functional approach to the nature of mathematical reality. It leaves room for the mystery without endorsing mysticism. As I discussed on WKU, this problem has really been the center of philosophy from the beginning: seeking truths as compelling as mathematical theorems in all inquiries.
The short answer: we are not endowed with a category for the ontological status of mathematical forms, so we apply the concept of existence as evolved. The long answer will require a book.
I must say I’m delighted to find such sitmulating thought in the first 20 pages, of more than 1000.