Elementary proof
From Wikipedia, the free encyclopedia
In mathematics a proof is said to be elementary if it avoids difficult ideas from distant areas of mathematics. For example, the term is used in number theory to refer to proofs that make no use of complex analysis. An elementary proof in combinatorics, using methods such as direct enumeration, is similarly called a "combinatorial proof".
The distinction between elementary and non-elementary proofs has been considered important in regard to the prime number theorem. It was first proved in 1896 by Jacques Hadamard and Charles Jean de la Vallée-Poussin using complex analysis. Many mathematicians then attempted to construct elementary proofs of the theorem. G. H. Hardy in 1921 expressed strong reservations; he considered that the essential 'depth' of the result ruled out elementary proofs. In 1948, Selberg produced new methods which led to elementary proofs of this result.[1]
[edit] References
- ^ Goldfeld, Dorian M. (2003). "The Elementary Proof of the Prime Number Theorem: An Historical Perspective" (PDF). Retrieved on 2007-11-14.
