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From: jbarnett@shomase.NoSubdomain.NoDomain (Jeff Barnett)
Subject: Re: Mathematics Theory Expert System
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References: <Pine.GSO.3.93.960917205041.23040C-100000@hamlet.uncg.edu> <32407627.78EC@postoffice.worldnet.att.net>
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Date: Mon, 23 Sep 1996 20:25:15 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai:41071 sci.math.num-analysis:30407

In article <32407627.78EC@postoffice.worldnet.att.net>, kenneth paul collins <KPCollins@postoffice.worldnet.att.net> writes:
|> QIAN . ZHONG wrote:
|> > 
|> > 
|> >  Hi, there:
|> > 
|> >  I am new to this field and I wonder if there is something like
|> > "Mathematics Theory Generating Expert System", which will generate new
|> >  math theme or prove a theme by itself, it can use induction, plausible

Doug Lenat's dissertation at Stanford, a decade or so ago, did just that.
It used heuristics about what would make a concept more interesting,
(e.g., if C applies to every thing, make C more specific) to determine
how much resources to apply to modify conceps.  It started with the
concepts of multi-sets (same element can appear many times), the
member-of primitive, and the heuristics.  It looked for interesting
conjectures, not proofs.  In my mind it was very successful: it
"discovered" the concepts of integers, prime numbers, correspondence,
etc.  Try to find a copy of the thesis if you want to read some
good stuff on the topic.

Jeff Barnett
