Kurt Gödel is certainly one of the biggest names of logic and mathematics of the last century. Besides that, he is also the most famous proponent of mathematical Platonism. The aim of this work is to investigate different aspects of Gödel's Platonism as well as arguments he put forward in its support. We shall see that despite the problems Platonism faces, there is a lot to cite that promotes it as the only viable position in the philosophy of mathematics.