Doug Lenat

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

• AM's remarkable successes were due in a sense to it starting with a notation amazingly well suited to making simple, interesting statements about mathematics -- in essence, due to Alonzo Church's brilliance in designing the lambda calculus.
• That "intelligent" behavior depends critically on having available a large stock of "common-sense" knowledge -- perhaps 100,000 rule's worth.

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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