The Eisenstein Criterion is a well-known sufficient condition for a polynomial with integer coefficients to be irreducible. What is less well-known is that Schoenemann discovered the criterion several years before Eisenstein. This lecture will explore the historical background of the developments, which includes the theory of finite fields and ruler and compass constructions on the lemniscate. There will be quotes from original works of Gauss, Abel, Eisenstein, Schoenemann, and others.