  The relationship between the complexity classes P and NP is an unsolved
question in the field of theoretical computer science. In this paper, we look
at the link between the P - NP question and the "Deterministic" versus "Non
Deterministic" nature of a problem, and more specifically at the temporal
nature of the complexity within the NP class of problems. Let us remind that
the NP class is called the class of "Non Deterministic Polynomial" languages.
Using the meta argument that results in Mathematics should be "time
independent" as they are reproducible, the paper shows that the P!=NP assertion
is impossible to prove in the a-temporal framework of Mathematics. In a
previous version of the report, we use a similar argument based on randomness
to show that the P = NP assertion was also impossible to prove, but this part
of the paper was shown to be incorrect. So, this version deletes it. In fact,
this paper highlights the time dependence of the complexity for any NP problem,
linked to some pseudo-randomness in its heart.
