We observe that a certain kind of algebraic proof-which covers essentially all known
algebraic circuit lower bounds to date-cannot be used to prove lower bounds against VP if
and only if what we call succinct hitting sets exist for VP. This is analogous to the Razborov-
Rudich natural proofs barrier in Boolean circuit complexity, in that we rule out a large class
of lower bound techniques under a derandomization assumption. We also discuss
connections between this algebraic natural proofs barrier, geometric complexity theory, and …