Consider that mathematics is invented in some predetermined way. Would it then still be possible to claim that it is really invented and not discovered? Is there a point, modulo determinism, where the invention/discovery distinction breaks down?
There is, for example, a BBC science article that says that mathematics is both invented and discovered. It says that truths are discovered and proofs are invented, to be precise. But sometimes, don't we speak of discovering proofs?
I would recommend Katz., et. al.'s "Interpreting the infinitesimal mathematics of Leibniz and Euler" for information pertinent to your question. I will quote from the text at a few points, to point you towards why I think this essay is pertinent.
Firstly, regarding the appearance (perhaps deceiving, then) of inevitability in the way mathematics has developed:
The butterfly/Latin distinction is:
Inspired in part by [Mancosu 2009], Ian Hacking proposes a distinction between the butterfly model and the Latin model, namely the contrast between a model of a deterministic biological development of animals like butterflies, as opposed to a model of a contingent historical evolution of languages like Latin. For a further discussion of Hacking’s views see Section 5 below.
To roughly sum things up: our experience of mathematical history is not clearly one where all future mathematical practices and ontology are hereditarily unfolded from past ones. There are both continuities and discontinuities in the development of both that seemingly tell against an overly deterministic picture of such development. Sometimes a newer theory inherits many of its characteristics from a previous one, as if genetically we might say; sometimes a newer theory breaks onto the scene like a star falling from heaven (I would picture some of Cantor's insights in this way, and he himself sometimes spoke as if God had revealed the transfinite numbers to him somehow from "on high").