One form of Platonism entails the actual existence of mathematical objects. Godel and others were known to feel intuitively that they were working with and actually perceiving entities different from, but every bit as "real" as, physical objects.
Other mathematicians have described their arrival at unexpected results as feeling like "experimental discovery." (Realism in Mathematics, Penelope Maddy) More to the point, I understand that there are now purely "experimental" branches of mathematics using computers, though I'm not sure what is involved here. This would seem to remove some of the subjectivity associated with talk of mathematical Platonism.
Have computers indeed enabled mathematicians to "experiment" in ways more analogous to the physical sciences? Does this constitute a stronger argument for the "reality" of mathematical objects? If we talk about "experimental mathematics" is this a form of Platonism or is it cognitive naturalism? Or either one? Odd, I had always imagined these two as complete opposites.