The Shuffle Conjecture gives a Combinatorial setting to the bi-graded Frobenius Characteristic of the Diagonal Harmonic Module of $S_n$. We report here on the progress in joint work with Angela Hicks in a three year effort to prove this conjecture. Angela Hicks reduced a combinatorial side of the problem to proving a deceptively simple property of a remarkable family of polynomials in a single variable $x$ with coefficients polynomials in $N[q]$. In this lecture and possibly following ones we describe what remains to be done to resolve this decade old Algebraic Combinatorial problem.