::But non-elementary proofs link these subjects in a non-elementary way, which casts some doubt if they are really connected. If they are ''real''-ly connected, then the link should be evident using real numbers and without resorting to complex numbers, or the Axiom of Choice or any of these other "additions" to mathematics that do not reflect the real world. The one good that I can attribute to a non-elementary proof is that it will make mathematicians search for an elementary proof of the same theorem. With some ingenuity they may find one, as Erdos and Selberg did with the Prime Number Theorem. -[[User:Foxtrot|Foxtrot]] 23:03, 12 September 2008 (EDT) | ::But non-elementary proofs link these subjects in a non-elementary way, which casts some doubt if they are really connected. If they are ''real''-ly connected, then the link should be evident using real numbers and without resorting to complex numbers, or the Axiom of Choice or any of these other "additions" to mathematics that do not reflect the real world. The one good that I can attribute to a non-elementary proof is that it will make mathematicians search for an elementary proof of the same theorem. With some ingenuity they may find one, as Erdos and Selberg did with the Prime Number Theorem. -[[User:Foxtrot|Foxtrot]] 23:03, 12 September 2008 (EDT) |