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]]. | + | 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]]. In contrast, [[Andrew Wiles]]' proof of [[Fermat's Last Theorem]] did not use elementary techniques and he did not receive the Fields Medal for his work but rather an honorary silver plate from the [[International Mathematical Union]].<ref>http://www.mathunion.org/medals/Fields/Prizewinners.html</ref> |
===Sources=== | ===Sources=== | ||
Revision as of 19:08, June 26, 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. In contrast, Andrew Wiles' proof of Fermat's Last Theorem did not use elementary techniques and he did not receive the Fields Medal for his work but rather an honorary silver plate from the International Mathematical Union.[2]