Changes

Jump to navigation Jump to search
390 bytes added ,  18:40, August 25, 2009
significance is two-fold
Line 2: Line 2:     
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]] is not an elementary proof.<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]] is not an elementary proof.<ref name="Occam">http://www.occampress.com/fermat.pdf Page 5</ref>
 +
 +
== Significance of Elementary Proofs ==
 +
 +
Elementary proofs are preferred over non-elementary proofs for at least two reasons:
 +
 +
*elementary proofs minimize the underlying assumptions, as in avoiding the assumption that there is a unique, algebraically manipulable square root of negative one
 +
*elementary proofs are typically impossible to simplify further in a logically significant manner
    
==References==
 
==References==
Anthony, Irenaeus, Siteadmin, Bureaucrats, Check users, nsAm_Govt_101RO, nsAm_Govt_101RW, nsAm_Govt_101_ta, nsJudgesRO, nsJudgesRW, nsJudges_talkRO, nsJudges_talkRW, nsTeam2RO, nsTeam2RW, nsTeam2_talkRO, nsTeam2_talkRW, oversight, Administrators
126,102

edits

Navigation menu