The “P-NP ” problem and the deterministic or time independent nature of Mathematics

The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. After a brief presentation, this paper looks at the relation between the P- NP question and the “Deterministic ” versus “Non Deterministic” nature of a problem. Let us remind that the NP class is called the class of “Non Deterministic Polynomial ” languages. Using the meta Mathematical argument that proofs should not have any reference to time, the paper shows that the P = NP assertion is impossible to prove in the deterministic or time independent framework of Mathematics. A similar argument based on Randomness shows that the P = NP assertion is also impossible to prove, so that the P- NP problem turns to be undecidable in the framework of Mathematics