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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.
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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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The prime number theorem has long been proven using complex analysis (Riemann's 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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===Sources===
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{{reflist}}
 
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'''Sources:''' <references/>
      
[[Category:Mathematics]]
 
[[Category:Mathematics]]
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