Discovering Quadratic Reciprocity Is there anything similar to this (page written by Field Medalist Timothy Gowers) for quadratic reciprocity ? 
I mean, the link there explains how you can figure out the solution of cubic equation by yourself without having a suddent flash of inspiration/ genius genes. Is there some similar guide for quadratic reciprocity ?

The first chapter of Cox's book, "Primes of the form $x^2+ny^2$", discusses the origins of quadratic reciprocity, and shows through the discussion and by extended examples how Euler was led to discover quadratic reciprocity from considerations of solutions to this equation for various $n$.
