A large part of intelligence
is the ability of your brain
to map out complex relationships between ideas. Simply knowing a lot of data doesn't make you smart or creative -- it's the structured connections you can make between all of those little discrete packets of data.
The brain is constantly toying with the information you absorb - trying out random connections, and seeing how they fit in. Little neurons firing, misfiring, whatever it is. Creative "eureka" moments come from making a random connection that no one else has made before, and all of the pieces suddenly fall into place.
So how does genius connect with mental instability? The average person makes a certain amount of random connections, and most of them get filtered out automatically because they don't fit into the limited mental maps that person has constructed. The "genius" has a lot more random connections, and they seriously consider a much larger proportion of them. They start new maps more often. They don't filter out ideas just because no one else has tried them before -- and sometimes something great is created.... but sometimes they have so many unfiltered random connections that they can't get through everyday life.
"Madness" could be a number of things in this model -- no filters on random connections, overactive filters (where almost all connections are filtered out as irrelevant), too many random connections, or too few.
Note: some of the ideas here (about mental maps vs. flat information) are taken from reciprocality.org.