It's been literal decades since I saw it, but the premise of K-Pax always seemed neat: aliens move their consciousness around through some sort of superliminal signal[1], but it looks an awful lot like madness to us humans.

Until he starts solving cosmological problems . . I sort of felt like the truth of the matter should have been more ambiguous than was presented. More Shining, less Friday the 13th.

I remember the premise being far superior to the film, but maybe the novel is worth a look.