>From the web pages of Alan Bundy:
http://www.dai.ed.ac.uk/staff/personal_pages/bundy/teaching/2-method/notes/ai2-meth-notes/node3.html
Bundy says the following quote can be found in:
Simon, H.A. and Newell, A. (1958). Heuristic problem solving: The next
advance in operations research. Operations Research, 6(1).
``On the basis of these developments, and the speed with which research in
this field is progressing, I am willing to make the following predictions,
to be realized within the next ten years:
1. That within ten years a digital computer will be the world's chess
champion, unless the rules bar it from competition.
2. That within ten years a digital computer will discover and prove an
important new mathematical theorem.
3. That within ten years a digital computer will write music that will be
accepted by critics as possessing considerable aesthetic value.
4. That within ten years most theories in psychology will take the
form of computer programs, or of qualitative statements about the
characteristics of computer programs.''
End quote
The development mentioned in prediction one arguably happened in 1997
(http://www.chess.ibm.com/). Of course, the match was not for the world
chess championship as recognized by a major chess organization, but
Kasparov is widely recognized as the best human chess player.
This event took 39 years after 1958 instead of ten.
The closest match for prediction two I can think of extemporaneously is
the proof that "Robbins Algebras Are Boolean"
(http://www.mcs.anl.gov/home/mccune/ar/robbins/index.html). A computer
program did not "discover" this theorem, but a program called an automated
deduction system was used to prove it.
Here is an excerpt from the press release announcing this result:
The Robbins problem, which has puzzled mathematicians and
logicians for more than 60 years, has been solved by automated
reasoning software developed in the Mathematics and Computer
Science Division of Argonne National Laboratory. The problem
was posed by Herbert Robbins at Harvard University in the
1930s, and some of the great mathematicians of the century
have worked on it.
End excerpt
The proof of Robbins Theorem was done in 1996. Other proofs such as the
"Four Color Map Theorem" and the "Non-existence of the Finite Projective
Plane of Order 10" required the use of computers and human thought.
Maybe some list member will know about a match or partial match for
prediction three.
Prediction four is not easy to assess because psychology is a diverse
field and the prediction refers to "most theories in psychology". Yet,
computer models of human thought are certainly influential nowadays. See,
for example, Steven Pinker's recent book "How the Mind Works" W. W.
Norton and Company (1997)
Gregory Sullivan