The Quadratic Reciprocity Law is, in my opinion, an example of a beautiful pattern in elementary Number Theory. As a result of work done in the early 20th century on the theory of algebraic numbers, this law finally inherited a structural interpretation as a corollary to a much more encompassing "reciprocity" law. My talk will attempt to make sense of this law, which is mainly due to Artin, by introducing the necessary concepts and objects in this brand of Algebraic Number Theory.
This talk should be accessible to those familiar with (abstract) algebra.