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Conservapedia:Critical Thinking in Math (view source)
Revision as of 03:03, September 13, 2008
, 03:03, September 13, 2008→Draft Curriculum: reply to KennyMac
*Regarding the lengthy discussion above, can I point out that non-elementary proofs, particularly if they are elegant, are especially valued by mathematicians because they draw together areas of knowledge which were previously thought to be unconnected. Elementary proofs, i.e. proofs which only draw on a small body of related concepts, don't do that - they may be easier to follow but they don't have the excitement of "sparking across the creative gap". [[User:KennyMac|KennyMac]] 19:04, 11 September 2008 (EDT)
*Regarding the lengthy discussion above, can I point out that non-elementary proofs, particularly if they are elegant, are especially valued by mathematicians because they draw together areas of knowledge which were previously thought to be unconnected. Elementary proofs, i.e. proofs which only draw on a small body of related concepts, don't do that - they may be easier to follow but they don't have the excitement of "sparking across the creative gap". [[User:KennyMac|KennyMac]] 19:04, 11 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)