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From: vlsi_lib@netcom.com (Gerard Malecki)
Subject: Re: Thought Question
Message-ID: <vlsi_libD3sys6.n3o@netcom.com>
Organization: VLSI Libraries Incorporated
References: <D3L5M9.Gx4@cogsci.ed.ac.uk> <vlsi_libD3LpyC.158@netcom.com> <D3rBqC.I1u@festival.ed.ac.uk>
Date: Fri, 10 Feb 1995 21:09:42 GMT
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In article <D3rBqC.I1u@festival.ed.ac.uk> cam@castle.ed.ac.uk (Chris Malcolm) writes:
>In article <vlsi_libD3LpyC.158@netcom.com> vlsi_lib@netcom.com (Gerard Malecki) writes:
>
>>While programs written in prolog can do deductive
>>inferences orders of magnitude faster than mathematicians, none has
>>been able to come anywhere close to giving constructive proofs like
>>for Fermat's theorem or Gleason's theorem, two of the many triumphs
>>of the human mind. 
>
>Just to give the AI people something to aim at, could you give us an
>estimate of the number of man-hours it took the mathematical community
>to prove Fermat's theorem?

I do not deny the fact that it took centuries for mathematicians to 
prove Fermat's theorem. But it was one man who finally proved it based
on previous work, within his lifetime (obviously). And since humans have
so many other duties to attend to, the actual number of man hours spent
by the mathematician who proved it may be significantly less. In contrast,
computers can devote their attention to the problem continuously for years
without getting bored or exhausted. Computers need not have to start from
scratch. They can take off from the current state of human knowledge.
This way, proving Fermat's theorem doesn't seem to be an unreasonable
goal for AI.

Shankar Ramakrishnan
shankar@vlibs.com
