From what I gather, for realists who are especially fond of a good old-fashioned Mathematical Platonism incorporated in their ontology, there seem to be two ways of getting at it. The first seems to be the need for truth-makers for mathematical propositions/truths, hence the positing of mathematical objects as abstract objects which serve as truth-makers. The other route is to marshal the Quine-Putnam Indispensability Argument, or some contemporary variation, and deduce their existence (am I right in thinking this is a deductive argument, or is it an abductive argument? Perhaps their are versions of both) by noting that the existential quantifier is a device for ontological commitment.
First of all, am I mistaken in thinking that these represent some of the motivations for adopting/positing Mathematical Platonism? Secondly, are there any other motivations for adopting/positing Mathematical Platonism?