The author brings up a good point. In mathematics, existence includes all possibilities and constructs that emanate from an axiomatic system. But in the universe as a whole, we have a time element - can we say the heat death of the universe is real and -exists- if it hasn't happened yet but is a forgone consequence of the universe's physical rules? Furthermore, if the origin of the universe is simply some simple rules that cause the notions of space and time and all the consequent physics - would we not abstract and say that the truest sense of the universe is then its simplest constituents - ie. the original mathematical rules that cast spacetime into existence? Math is all about generalizing and abstracting to more universally applicable truths. It is the science of pure truth. And I also believe that human instinct of seeking higher platitudes of knowledge is also based on abstracting ideas and truths in more generally applicable forms. Ultimately our concious experience is filtered by our Phaneron [1]. So it is hard to be concrete on an opinion about the universe when our own model of cognition is much more limited and thus a smaller universe of discoverable truth. That is where faith exists. I liken wisdom about full truth to be best described by buddhists, if the universe is all form, the origin of form, then it is impossible to see its form from the outside. [2] Recursion and self description is the origin of all antimonies. One cannot fully perceive the black box that one is an inhabitant of. The outside perspective, the true non shadowed clockwork, will always be a mystery.
[1] https://en.m.wikipedia.org/wiki/Phaneron
[2] https://en.m.wikipedia.org/wiki/Skolem%27s_paradox