The Jargon File (version 4.4.7, 29 Dec 2003):

Infinite-Monkey Theorem
 n.

    ?If you put an infinite number of monkeys at typewriters, eventually one
    will bash out the script for Hamlet.? (One may also hypothesize a small
    number of monkeys and a very long period of time.) This theorem asserts
    nothing about the intelligence of the one random monkey that eventually
    comes up with the script (and note that the mob will also type out all the
    possible incorrect versions of Hamlet). It may be referred to
    semi-seriously when justifying a brute force method; the implication is
    that, with enough resources thrown at it, any technical challenge becomes a
    one-banana problem. This argument gets more respect since Linux
    justified the bazaar mode of development.

    Other hackers maintain that the Infinite-Monkey Theorem cannot be true ?
    otherwise Usenet would have reproduced the entire canon of great literature
    by now.

    In mid-2002, researchers at Plymouth Univesity in England actually put a
    working computer in a cage with six crested macaques. The monkeys proceeded
    to bash the machine with a rock, urinate on it, and type the letter S a lot
    (later, the letters A, J, L, and M also crept in). The results were
    published in a limited-edition book, Notes Towards The Complete Works of
    Shakespeare. A researcher reported: ?They were quite interested in the
    screen, and they saw that when they typed a letter, something happened.
    There was a level of intention there.? Scattered field reports that there
    are AOL users this competent have been greeted with well-deserved
    skepticism.

    This theorem has been traced to the mathematiciamn ?mile Borel in 1913, and
    was first popularized by the astronomer Sir Arthur Eddington. It became
    part of the idiom of techies via the classic SF short story Inflexible
    Logic by Russell Maloney, and many younger hackers know it through a
    reference in Douglas Adams's Hitchhiker's Guide to the Galaxy. Some other
    references have been collected on the Web. On 1 April 2000 the usage
    acquired its own Internet standard, RFC2795 (Infinite Monkey Protocol
    Suite).