Difference between revisions of "Elementary proof"
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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]]. In contrast, [[Andrew Wiles]]' proof of [[Fermat's Last Theorem]] did not use elementary techniques.<ref name="Occam">http://www.occampress.com/fermat.pdf Page 5</ref> | 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.<ref name="Occam">http://www.occampress.com/fermat.pdf Page 5</ref> | ||
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[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 00:23, January 30, 2009
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] An elementary proof typically cannot be improved by expressing it in simpler form.
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.[2]
