Directed polymers are a statistical mechanics model for random growth.  Their partition functions are solutions to a discrete stochastic heat equation.  This talk will discuss their logarithmic derivatives, which are solutions to a discrete stochastic Burgers equation.  Of interest is the success or failure of the  “one force-one solution principle” for this equation.  I will reframe this question in the language of polymers, and share some surprising results that follow.  No background in differential equations is necessary.  Based on joint work with Louis Fan and Timo Seppäläinen.