I probably incorrectly understand some basic things, so I'll show my layman thinking process for easier identification of where lies the problem.
Let's start with basic dichotomy - materialism vs. idealism of what's more primal - matter or mind. As far as I understand, idealism operates only on concepts of human mind and perception thus it's strictly anthropocentric approach.
As materialism states that only matter ontologically exists, idealism states that only ideas (i.e. human cognitive apparatus and perception) ontologically exist.
Thus if we want to stick with idealism, we fall into correlation loop - we are constricted by the ideas we are able to think, as if we assume something that we can't think, it automatically becomes thinkable.
So if idealist wants to say that some object "exists" that would mean something like "we are able think that this object exist (exist in intersubjective consensus reality)".
Then Plato's states his Forms - entities that are not material objects (thus, it's not a materialism), but also not a results of human mind, as they ontologically exist, independent from our cognition. So why is it idealism? Forms doesn't fall in any category of mind and matter. Is it implicitly assumed that Form are results of human cognition? In another words, who thinks the Forms for them to exist in idealistic approach?
As far as I understand, by Plato "actual" reality constitutes only from From, by they are inaccessible by any meaning. Would it be correct to say that the Form might as well not exist at all from this standpoint?
Why does Platonism falls into a mathematicism category? If we say that everything is math concepts, not correlated with human perception and cognition, wouldn't it be a materialism?