  This is an introduction, aimed at a general mathematical audience, to recent
work of Aprodu, Farkas, Papadima, Raicu and Weyman. These authors established a
long-standing folk conjecture concerning the equations defining the tangent
developable surface of a rational normal curve. This in turn led to a new proof
of a fundamental theorem of Voisin on the syzygies of a general canonical
curve. The present note, which is the write-up of a talk given by the second
author at the Current Events seminar at the 2019 JMM, surveys this circle of
ideas.
