I asked an almost exact question on History of Science and Mathematics SE. I vaguely remember reading a quote/listening to a statement by (I think) John Conway which I can paraphrase as follows:
"I do not know what object the Monster group acts on, but it seems to exist because string theory needs/wants/demands it."
Unfortunately, I do not know whence this quote comes, nor do I know the exact phrasing. Does anyone know of the quote to which I am referring, and perhaps has a reference? I was hoping to use this as an epigraph in my doctoral thesis if I can find a source and exact quote.