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From: smythe@iuvax.cs.indiana.edu
Newsgroups: comp.ai
Subject: Re: The Success of AI
Message-ID: <12400005@iuvax>
Date: Tue, 20-Oct-87 15:46:00 EDT
Article-I.D.: iuvax.12400005
Posted: Tue Oct 20 15:46:00 1987
Date-Received: Wed, 21-Oct-87 23:18:05 EDT
References: <1922@gryphon.CTS.COM>
Organization: Indiana University CSCI, Bloomington
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Nf-From: iuvax.cs.indiana.edu!smythe    Oct 20 14:46:00 1987


> /* Written  5:09 pm  Oct 17, 1987 by eric@snark in iuvax:comp.ai */
> 
> ...
> 
> Doug Lenat's Amateur Mathematician program was a theorem prover equipped with
> a bunch of heuristics about what is 'mathematically interesting', essentially
> methods for grinding out interesting generalizations and combinations of known
> theorems. Lenat fed it the Zermelo-Frankel set theory axioms and let it run.
> 
> After n hours of chugging through a lot of nontrivial but already-known
> mathematics, it 'conjectured' and then proved a bunch of new results on the
> number-theoretic properties of Pythagorean triples (3-tuples of integers of 
> the form <x, y, sqrt(x**2 + y**2)>).
> 
> I was a theoretical mathematician at the time I saw the AM paper. It was
> *fascinating*. The program could probably have done a lot more, but it
> eventually choked on the size of its own LISP data structures.
> 
> So at least one of your negative assertions is incorrect.

The reason that AM choked was not so much that it got bogged down in
its data structures, but that its ``discovery heuristics'' kept it
from discovering anything ``interesting'' (by its own measure) after
a while.  It simply started thrashing without making much progress.
EURISKO was an attempt to remedy that by discovering or refining its 
own heuristics.  Read Lenat's paper, ``The Nature of Heuristics'' for
his own explanation.

Erich Smythe
Indiana University
smythe@iuvax.cs.indiana.edu