This paper discusses different forms of mathematical realism and especially different kinds of advocating realistic position. Husserl’s phenomenological approach, Gödel’s (phenomenological and) methodological approach and Quine’s naturalistic approach are presented. Afterwards, Maddy’s realism is reconstructed as a synthesis of Gödel’s and Quine’s views, overcoming weaknesses of both. Also Maddy’s later rejection of her own realism and its replacement by naturalistic project are discussed. At the end, we are offering our own interpretation of the problem of realism in mathematics.