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From: vlsi_lib@netcom.com (Gerard Malecki)
Subject: Re: Thought Question
Message-ID: <vlsi_libD40qHJ.IyG@netcom.com>
Organization: VLSI Libraries Incorporated
References: <3hgtj4$vk@romulus.rutgers.edu> <3hnf9q$qtp@oznet03.ozemail.com.au> <3hp6o6$9co@romulus.rutgers.edu>
Date: Wed, 15 Feb 1995 01:51:19 GMT
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In article <3hp6o6$9co@romulus.rutgers.edu> wclark@romulus.rutgers.edu (Bill Clark) writes:
>Alan Tonisson <tonisson@ozemail.com.au> writes:
>
>>> I doubt any serious consideration will ever be given to the task of
>>> designing computer alogorithms to replace human mathematicians.  Formalism
>>> is more of an afterthought in mathematics rather than the starting point,
>>> and in any event is an eventual dead end unto itself.  The only way I see
>>> a computer program capable of solving problems of the same relative
>>> complexity or difficulty as FLT is when problems of that caliber become
>>> trivial to human mathematicians, which I don't see happening for a 
>>> *very* long time.
>
>>I'm a mathematician, and I don't believe that what we mathematicians do is
>>so mysterious that it can't be taught to a machine.  In each field of
>>mathematics there are heuristics for finding proofs.  They are hard to write
>>down but, given time, they could be coded.
>
>I didn't claim that they couldn't be taught to a machine.  I was simply
>expanding upon the same idea you just mentioned: They (the heuristics) are
>hard to write down.  For problems such as FLT, I can't even begin to
>imagine how complex the algorithm that could solve problems of this "type"
>would be.  The point isn't that such an algorithm can't be produced, its
>simply that by the time mathematics advances to the point where it *can*
>supply the algorithm, there won't be much point in having a computer
>execute it.

This would be true of most algorithms existing today. However we can come
up with evolutionary algorithms which would learn from past experience
and come up with more and more sophisticated methods of reasoning than
what the programmer had in mind. That would be the cornerstone of AI.
(After all, Newton wasn't taught calculus in school.)

Shankar Ramakrishnan
shankar@vlibs.com
