Hilbert's syzygy theorem implies that the second syzygy of every module over a polynomial ring S in two variables is projective. In fancy language, this means that $Ext_S^3(M,N)$ vanishes for every pair of modules $M,N$. This is no longer true when we consider a quotient $R$ of $S$ by an ideal generated by a single polynomial $f$. In fact, for every $i>0$ there is at least one pair $M,N$ such that $Ext_R^i(M,N)\neq 0$. We investigate the ideal consisting of ring elements which uniformly annihilate all $Ext_R^i(M,N)$ for sufficiently large $i$. I am dedicating this talk to students and academics of Boğaziçi University who are protesting against a rector appointed by the 12th president of Turkey and I will try my best to keep it accessible to a broad audience.