I did not know that there were proofs of the "Buttered Toast" problem !
Now I know what I'm gonna read over the time I can't get into office to do research (aka easter)!
Then again, there's been honest research on the way slinkies move (paper called: On Slinky Dynamics) and on how the cats fall down (that's some great math and physics!), so buttered toast isn't really that out of the ordinary.