Quadratic reciprocity was first proved by Gauss, and in Disquisitions Arithmeticae he calls it the "Fundamental Theorem." In this talk, we will motivate quadratic reciprocity with some of the ideas and conjectures of Fermat, Euler, and Legendre. I will present a proof that is relatively short and requires only a familiarity with groups, rings, and fields to understand. The goal of this talk is to give an appreciation for a useful and historically significant theorem, so I aim for it to be very accessible.
A Proof of Quadratic Reciprocity