IN SEPTEMBER 1957, Herbert Simon, a pioneer in cognitive simulation, predicted that within ten years, i.e., by now, a computer would be world chess champion and would prove an important mathematical theorem. This prediction was based on Simon's early initial success in writing a program that could play legal chess and one able to prove simple theorems in logic and geometry. But the early successes turned out to be based on the solution of problems that were simple for machines, and (...) further progress turned out to be more and more difficult, until recently it has begun to be obvious to interested observers, and even to some workers in the field, that the original optimism of Simon and company was unfounded. (shrink)