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.