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For questions related to 'elementary' proofs in a technical sense, which has nothing to do with the difficulty of the argument or result. A typical example would be 'elementary' proofs of the Prime Number Theorem, which avoid complex analysis. The tag is however not limited to this particular notion of 'elementary.'
27
votes
Unrigorous British mathematics prior to G.H. Hardy
These examples relate to algebra rather than analysis, but might in any case be useful.
The papers of JJ Sylvester are full of deep insight and entertaining prose, but are also full of unsupported cla …