ABSTRACT
The Law of Quadratic Reciprocity is one of the high points of number theory. It was conjectured by Leonhard Euler and Adrien-Marie Legendre. In 1796, when he was 18 years old, Karl Friedrich Gauss gave the first proof. Gauss published six proofs during his lifetime, and two more were found in his unpublished manuscripts. Attempts to generalize Quadratic Reciprocity inspired the development of algebraic number theory in the 1800s and 1900s, and greatly influenced modern areas of research such as elliptic curves and modular forms from the 1900s up to the present. Quadratic Reciprocity is a useful computational tool, as seen, but it has a deeper significance. The proof of Quadratic Reciprocity is rather technical and can easily be skipped without impairing the understanding.
