Changes

The term "elementary proof" or "elementary techniques" in mathematics means use of only [[real numbers]] rather than [[complex numbers]], which relies on manipulation of the imaginary square root of (-1).  Elementary proofs are preferred because they are do not require additional assumptions inherent in complex analysis, such as that there is a unique square root of (-1) that will yield consistent results.

The term "elementary proof" or "elementary techniques" in mathematics means use of only [[real numbers]] rather than [[complex numbers]], which relies on manipulation of the imaginary square root of (-1).<ref>http://mathworld.wolfram.com/ElementaryProof.html</ref> Elementary proofs are preferred because they are do not require additional assumptions inherent in complex analysis, such as that there is a unique square root of (-1) that will yield consistent results.

Mathematicians also consider elementary techniques to include objects, operations, and relations.  Sets, sequences and geometry are not included.

Mathematicians also consider elementary techniques to include objects, operations, and relations.  Sets, sequences and geometry are not included.

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.

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.