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*> In a discussion in another forum, the question of whether computers have
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*> "found" valid mathematical proofs has come up. Being mathematically stunted,
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*> I thought I'd do a hand-off of the question to this forum, since someone able
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*> to comment intelligently on the question probably inhabits this forum. Any
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*> leads or help?
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The scare quotes seem appropriate, because it really depends on what you

mean by "found". After all, humans programmed systems to search for

proofs, and generally directed them in what to look for, so I'd be more

inclined to say that human mathematicians found the proofs with the aid

of a computer (and which they would not have found without such aid).

The classic case is the four-color threorem: a computer was used to

enumerate and evaluate a large collection of maps, and then prove by

time-consuming brute force that a specific subset of the ones generated

exhausted all relevant possibilities. A human could not have done this

within a lifetime.

Similar programs have also "found" interesting theorems and their

proofs, given sufficient guidance from human programmers as to what

is "interesting", without specifically being told what to look for.

-- Lee Daniel Crocker <lee@piclab.com> <http://www.piclab.com/lee/> "All inventions or works of authorship original to me, herein and past, are placed irrevocably in the public domain, and may be used or modified for any purpose, without permission, attribution, or notification."--LDC

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