I've talked to a fair number of mathematicians down through the years and the vast majority I've talked to are Platonists. Some have even thought about this stuff and know what Platonism means and assert that they are Platonists.
For me, once you read up on L.E.J. Brouwer's intuitionism and think through its consequences properly you can't be a Platonist, but that's just me – I undoubtedly have a prior more fundamental belief that makes me think this way. Like, I think it'd be difficult to be a (mathematical) Platonist and an atheist at one and the same time, but many mathematicians are.
For me, once you read up on L.E.J. Brouwer's intuitionism and think through its consequences properly you can't be a Platonist, but that's just me – I undoubtedly have a prior more fundamental belief that makes me think this way. Like, I think it'd be difficult to be a (mathematical) Platonist and an atheist at one and the same time, but many mathematicians are.