In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some time it was thought that certain theorems, like the prime number theorem, could only be proved using "higher" mathematics. However, over time, many of these results have been reproved using only elementary techniques.
While the meaning has not always been defined precisely, the term is commonly used in mathematical jargon. An elementary proof is not necessarily simple, in the sense of being easy to understand: some elementary proofs can be quite complicated.
Read more about Elementary Proof: Prime Number Theorem, Friedman's Conjecture
Famous quotes containing the words elementary and/or proof:
“Listen. We converse as we live—by repeating, by combining and recombining a few elements over and over again just as nature does when of elementary particles it builds a world.”
—William Gass (b. 1924)
“The proof of a poet is that his country absorbs him as affectionately as he has absorbed it.”
—Walt Whitman (1819–1892)