  Let $X\subset\mathbb{P}^{hn+h-1}$ be an irreducible and non-degenerate
variety of dimension $n$. The Bronowski's conjecture predicts that $X$ is
$h$-identifiable if and only if the general $(h-1)$-tangential projection
$\tau_{h-1}^X:X\dashrightarrow\mathbb{P}^n$ is birational. In this paper we
provide counterexamples to this conjecture. Building on the ideas that led to
the counterexamples we manage to prove an amended version of the Bronowski's
conjecture for a wide class of varieties and to reduce the identifiability
problem for projective varieties to their secant defectiveness.
