In this paper I investigate the question whether mathematical realism is compatible with Husserl's transcendental phenomenological idealism. The investigation leads to the conclusion that a unique kind of mathematical realism that I call "constituted realism" is compatible with and indeed entailed by transcendental phenomenological idealism. Constituted realism in mathematics is the view that the transcendental ego constitutes the meaning of being of mathematical objects in mathematical practice in a rationally motivated and non-arbitrary manner as abstract or ideal, non-causal, unchanging, non-spatial, and so on. The task is then to investigate which kinds of mathematical objects, e.g., natural numbers, real numbers, particular kinds of functions, transfinite sets, can be constituted in this manner. Various types of founded acts of consciousness are conditions for the possibility of this meaning constitution.