Some time ago (around 1998), a co-worker told me about a book that revolved around the Infinite Monkey Thereom. The protagonist was somehow made the manager of the project, in which he had to start over multiple times due to the monkeys messing something up near the finish line. I couldn't find it via Google search. Does this sound familiar to anyone?
R.A. Lafferty's "Been a Long, Long Time" seems like a potential good match.
It's a very well-written humorous tale (as expected if you're familiar with Lafferty). The mathematical content is a literal interpretation of the six typing monkeys. The angel Boshel, as a punishment, is assigned to supervise the project until the randomly-typing monkeys produce a perfect copy of the collected works of Shakespeare. The four and a half pages of the story follow the project through immense vistas of time, though not to completion. The story appeared in the December 1970 issue of Fantastic, and has been reprinted several times, e.g. in the anthology "Galactic Empires Volume One" by Brian W. Aldiss.
I personally find this summary even more enlightening, albeit that the page is more general:
In Lafferty's short "Been a Long, Long Time", a hapless immortal called Boshel accidentally introduces randomness into the newly created universe. His punishment is to test the theory that a team of monkeys typing at random could eventually produce the works of Shakespeare. In real time. The archangel Michael provides a clock, a stone cube light-years across:
"'You don't have to wind it, you don't have to do a thing to it, Bosh,' Michael explained. 'A small bird will come every millennium and sharpen its beak on the stone. You can tell the passing of time by the diminishing of the stone. It's a good clock and it has only one moving part, the bird ...'"
The task is still incomplete when the stone has worn away enough to accommodate a small solar system ...