%0 Journal Article %T The flecnode polynomial: a central object in incidence geometry %A Nets Hawk Katz %J Mathematics %D 2014 %I arXiv %X We give a brief exposition of the proof of the Cayley-Salmon theorem and its recent role in incidence geometry. Even when we don't use the properties of ruled surfaces explicitly, the regime in which we have interesting results in point-line incidence problems often coincides with the regime in which lines are organized into ruled surfaces. %U http://arxiv.org/abs/1404.3412v1