Hayley Reid, Department of Pure Mathematics, University of Waterloo
"The Law of Quadratic Reciprocity"
The law of quadratic reciprocity is a result in Number Theory about the solvability of quadratic equations modulo a prime p. The law was first proved in 1801 by Gauss, who then proceeded to provide 6 more proofs. Since then, there have been over 200 (!!) distinct proofs of the law of quadratic reciprocity, by mathematicians such as Eisenstein, Cauchy, Lebesgue, Dirichlet, Kummer, Dedekind, and many many more. So what makes this particular law so important that people are interested in continuing to find new proofs? In this talk we will give a brief overview of the history of the problem, discuss a few of the different techniques used in the various proofs, and talk about the far reaching implications and applications of this result.
MC 5417