Brouwer was supported by people like Weyl, and Gödel, but Hilbert's formulation came out on top, leading to the expulsion of time from mathematics, and mathematical objects were thus seen as objects that exist in some platonic realm.
We see reference to this in Leo Szilard's contemplation of Maxwell's Daemon, however this did not end the debate about the nature of information, and its physicality. Roger Penrose, in a rather Platonist, manner, upholds that "...devices can yield only approximations to a structure that has a deep and 'computer-independent' existence of its own.