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:::Your definition of an elementary proof does not withstand scrutiny for the reasons I stated, which you did not address.--[[User:Aschlafly|Andy Schlafly]] 11:46, 25 August 2009 (EDT)
:::Your definition of an elementary proof does not withstand scrutiny for the reasons I stated, which you did not address.--[[User:Aschlafly|Andy Schlafly]] 11:46, 25 August 2009 (EDT)
::::The proof in question (Selberg) was elementary by either standard, so I don't think that's relevant here. 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)