What message does Sophocles' Oedipus Tyrranus convey about the limits of human intellect?
Aristotle describes the tragic hero as a person better or greater than the average but with a fatal flaw. In the case of Oedipus, he appears a good ruler and benefactor of Thebes, attempting to solve the mystery of the plague in an intelligent fashion by striving to discover its cause. And yet, despite his best efforts, there can be no satisfactory resolution.
First, the curse on the House of Thebes is a divine punishment for impiety and cannot be evaded by mere mortal strategems.
Second, Oedipus himself is far from blameless. He did not need to offer violence to the old man at the crossroads (who was actually, unbeknownst to him, his own father). His own character leads him to his fate.
Third, when Tireisias, an infallible prophet and mouthpiece of the gods, warns him to cease his inquiries, Oedipus does not desist. Of course, he needed to persist to save the city -- it is the dilemma of there being no easy choices that makesa this a tragedy. Part of the tragic vision is that many situations do not have any possible happy ending.
Finally, when Oedipus does reform himself and gain wisdom, in Oedipus at Colonus, the curse is resolved, and true wisdom (intellect combined with ethics and peity) does lead to a successful reconciliation of gods and man.