  Recent work on the Jensen polynomials of the Riemann xi-function and its
derivatives found a connection to the Hermite polynomials. Those results have
been suggested to give evidence for the Riemann Hypothesis, and furthermore it
has been suggested that those results shed light on the random matrix
statistics for zeros of the zeta-function. We place that work in the context of
prior results, and explain why the appearance of Hermite polynomials is
interesting and surprising, and may represent a new type of universal law which
refines M. Berry's "cosine is a universal attractor" principle. However, we
find there is no justification for the suggested connection to the Riemann
Hypothesis, nor for the suggested connection to the conjectured random matrix
statistics for zeros of L-functions. These considerations suggest that Jensen
polynomials, as well as a large class of related polynomials, are not useful
for attacking the Riemann Hypothesis. We propose general criteria for
determining whether an equivalence to the Riemann Hypothesis is likely to be
useful.
