My answer to a question on Quora: Why are so many mathematicians platonists?
Because mathematics is consistent (or, at least, so far has been consistent). Even more so, it is more consistent than the “reality” as we see it around us, or hear other people talking about. At an ordinary, everyday level, our vision of the “real” world is full of contradictions, ambiguities, uncertainties, and — the last but not least — direct and intentional lies. In comparison with that mess, our vision of mathematics is crystal clear. Subjectively, mathematics can be perceived as something more real than the world around us.
Please notice that I do not claim that the Platonic world on mathematical objects exists. I am talking only about perception of mathematics by working mathematicians. Almost everyone who I know is, to some degree, a Platonist.