There was a comic book in the 80's called "Shatter" (greatly publicised because it was the first comic drawn and produced electronically) that had an ongoing plot about stealing memory RNA from experts and injecting it into other people. (Suspend your disbelief by the neck until dead.) While the story wasn't all that great, I remember the hero's comment that every discipline he thus acquired made him more dangerous, in that each gave him ways to organise data and solve problems, whether the "stolen" expertise was in chemistry or violin making.
I took a broad mix of Math, Economics and English in college and I think they each gave me problem solving tools. While Math may be the more obvious choice, the Economics classes gave me some practical grounding in gathering data (and in how silly the results can be if data is gathered selectively or if assumptions are made early in the process). A literature background will remind you that it's all been done before, if nothing else :)
Some of the best programmers I've known had no formal background in computer science. And some of the worst were CS majors, but I won't make assumptions :)