  Notions of rank abound in the literature on tensor decomposition. We prove
that strength, recently introduced for homogeneous polynomials by
Ananyan-Hochster in their proof of Stillman's conjecture and generalised here
to other tensors, is universal among these ranks in the following sense: any
non-trivial Zariski-closed condition on tensors that is functorial in the
underlying vector space implies bounded strength. This generalises a theorem by
Derksen-Eggermont-Snowden on cubic polynomials, as well as a theorem by
Kazhdan-Ziegler which says that a polynomial all of whose directional
derivatives have bounded strength must itself have bounded strength.
