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reply to Mark
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::::I don't wish to argue about what would be the best definition of an elementary proof, or the importance elementary methods, which I appreciate.  I just want to point out that the definition of "elementary proof" given here is not actually how the term is used in the mathematical literature, and I have supported this with a citation.  As such I think this page needs some adjustment -- it gives a definition of "elementary proof" which is used, as far as I can tell until you provide a citation, by no one except you.  It's quite possible that this would be a superior usage of the term, and I have no problem with the ideas on the page as it stands.  I would only ask to add a disclaimer that when mathematicians use the term "elementary proof", this is not always what they mean (as indicated by the AoC example above). --[[User:MarkGall|MarkGall]] 11:58, 25 August 2009 (EDT)
 
::::I don't wish to argue about what would be the best definition of an elementary proof, or the importance elementary methods, which I appreciate.  I just want to point out that the definition of "elementary proof" given here is not actually how the term is used in the mathematical literature, and I have supported this with a citation.  As such I think this page needs some adjustment -- it gives a definition of "elementary proof" which is used, as far as I can tell until you provide a citation, by no one except you.  It's quite possible that this would be a superior usage of the term, and I have no problem with the ideas on the page as it stands.  I would only ask to add a disclaimer that when mathematicians use the term "elementary proof", this is not always what they mean (as indicated by the AoC example above). --[[User:MarkGall|MarkGall]] 11:58, 25 August 2009 (EDT)
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::::: Mark, the entry does describe the traditional and only meaningful definition of "elementary proof."  Your definition, which is also used by Wikipedia, is non-substantive and cannot explain why the prestigious Fields Medal was given for it.  Nor does your definition explain why Paul Erdos, perhaps the most prolific mathematician of the 20th century, was such a stickler in preferring elementary proofs.
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::::: Perhaps there are some new mathematicians who are in denial about the importance of elementary proofs.  There are also new physicists who deny the importance of [[falsifiability]].  But self-described experts do not get to be the only watchdogs for their fields.  Some accountability can and should come from outside the fields of expertise.--[[User:Aschlafly|Andy Schlafly]] 12:23, 25 August 2009 (EDT)
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