Doug Lenat wrote possibly the most interesting program yet to come out of the artificial intelligence field: AM (2).
AM was a program to propose interesting mathematical theorems. Not to prove them: The artificial intelligence field is rife with programs that try to prove theorems, almost all of them uninteresting. AM had no concept of proof, it simply proposed theorems, more or less on intuition.
AM ran on a PDP-10 (the standard lisp machine in those days) and started with a small nucleus of concepts, plus a set of rules for specializing and generalizing concepts, and deciding how interesting they are. It kept a prioritized list of interesting things to investigate, and cyclically tried one of the most interesting and then added to the list any further ideas resulting.
Starting from its small nucleus of ideas from set theory, AM could discover among other things counting, addition, multiplication, prime numbers and Goldbach's Conjecture, which it would suggest to be true but uninterestng.
Perhaps most interestingly, it would invent the opposite of
prime numbers -- maximally divisible numbers -- and trot off
to propose theorems about them. Why is this interesting?
First of all, because Doug didn't know anything about such
numbers when he wrote the program, and in fact thought the
program was barking up an empty tree when it went that
direction. Secondly, because the theorems did indeed turn
out to be interesting, and for awhile it was thought that
this might be the first example of a computer program doing
interesting original mathematics. Thirdly, because it did
eventually turn out that
am had been anticipated
... by none other than Srinivasa Ramanujan, a
self-taught Indian genius who is arguably the greatest
natural talent mathematics has seen -- and who, like
AM, excelled at arithmetic computation while having
almost no concept of what a proof is.
Both AM's successes and failures have been dissected in some detail by the artificial intelligence community. (It never accomplished much else, and wasn't able to adapt very well to other problem domains.) Doug eventually concluded that
Whereup he trotted off to code up those 100,000 or so rules, and has hardly been heard of since. (Although he did pause long enough to win a national computer wargame competition by what might nowadays be called genetic programming: His computer search evolved a fleet design sufficiently convincing that most of his opponents resigned before a shot was fired, and the competition rules got changed the next year to close the loophole...)
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