And in 1963 Alan Robinson suggested the idea of resolution theorem proving, in which one constructs ¬ theorem ∨ axioms , then typically writes this in conjunctive normal form and repeatedly applies rules like ( ¬ p ∨ q) ∧ (p ∨ q)  q to try to reduce it to False , thereby proving given axioms that theorem is True .

And indeed the same seems to be true for traditional mathematical notation, where occasional deviations from the context-free model in fields like logic seem to make material particularly hard to read.

But it has never been entirely clear which of them are in a sense true defining features of quantum phenomena, and which are somehow just details.

(For n < 512 , this is true when n = 1 , 2 , 3 , 4 , 6 , 7 , 9 , 15 , 22 , 28 , 30 , 46 , 60 , 63 , 127 , 153 , 172 , 303 or 471 . … The largest m less than 2 16 for which this is true is 65063, and the sequence generated in this case appears to be fairly random.

(A fairly stringent example is 0 ≤ p ≤ ρ /3 —and whether this is actually true for non-trivial interacting quantum fields remains unclear.)

(The same is not true of simultaneous quadratic Diophantine equations, and indeed with a vector x of just a few variables, a system m . x 2  a of such equations could quite possibly show undecidability.)

(This seems to be true only in 2D, and not in 3D or higher.)