Non-Deterministically Polynomial (NP) and Polynomial (P)

Peruse the notes on heuristics. They provide the background on this "mental mathematical block" that has been placed squarely upon the noggin of modern computer science's pride-swollen head.

This modern misinterpretation and misunderstanding of the "heuristic" problem-statement has left the field at a "great loss".

Clever-insights, empirical-study, and innovative-intution make problems such as that of "finding a single cliqué" or "enumerating all of the cliqués" in a simple undirected-graph amenable.

• Cliqué emerge through the use of primitve values, the concept of a highest common factor, and pairwise refinement.
• CNF-SAT answers in the affirmative when cast it in the "bright and simple light" of DNF-SAT.
• Integer Knapsacks offer up solutions when described as a Diophantine equation and solved as a minimization-problem.
• SIS was originally cast as a deriviate of the cliqué.

In short, these are not "impossible". And truly, by the standards of accomplished mathematicians, these are not "difficult". Which is a synonym for "intractable".