Difference between revisions of "Elementary proof"
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An '''elementary proof''' or '''elementary technique''' in mathematics is a [[proof]] that uses only [[real numbers]] or [[real analysis]] rather than the use of [[complex analysis]].<ref>http://mathworld.wolfram.com/ElementaryProof.html</ref> Elementary proofs cannot be broken down into smaller proofs of the same proposition. | An '''elementary proof''' or '''elementary technique''' in mathematics is a [[proof]] that uses only [[real numbers]] or [[real analysis]] rather than the use of [[complex analysis]].<ref>http://mathworld.wolfram.com/ElementaryProof.html</ref> Elementary proofs cannot be broken down into smaller proofs of the same proposition. | ||
| + | The [[Prime Number Theorem]] has long been proven using complex analysis ([[Riemann Zeta function]]), but in 1949 and 1950 an elementary proof by [[Paul Erdos]] and [[Atle Selberg]] earned Selberg the highest prize in math, the [[Fields Medal]]. | ||
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[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 18:43, June 12, 2008
An elementary proof or elementary technique in mathematics is a proof that uses only real numbers or real analysis rather than the use of complex analysis.[1] Elementary proofs cannot be broken down into smaller proofs of the same proposition.
The Prime Number Theorem has long been proven using complex analysis (Riemann Zeta function), but in 1949 and 1950 an elementary proof by Paul Erdos and Atle Selberg earned Selberg the highest prize in math, the Fields Medal.