In this paper:https://dl.acm.org/doi/pdf/10.1145/62212.62241, what's given is $P(x)$ a (sparse) multivariate polynomial with real(or complex) coefficients. 
The author claimed two things. 
1. It is known that the problem of determining the exact number of monomials in $P(x)$ given by a black-box is #P-Complete (Kaltofen 1986).
2. It turns out that one can not determine the number of monomials $t$ in $P(x)$ in time $t^{O(l)}$ (or $t^{O(1)}$, can not see quite clearly).

How to understand these? Is there any proof or reference? Does it mean that it is computationally infeasible to determine the number of monomials in $P(x)$?
How will it be if the coefficients are taken from finite fields?

Does it mean that when evaluating at $2t$ points, if the Hankel matrix generated by these points has full rank, it is computationally infeasible to know what the exact number of monomials is?