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P=NP is, perhaps, the question of computer science and many related fields including logic and set theories. Much as Fermat’s Last Theorem has, the question of N=P has defied any resolution consensus among the individuals most widely asked to judge proposed solutions. Nor fame nor fortune nor sheer geeky pride has elicited, in the modern Western world, an acceptable solution.

(read about the Clay Mathematics Institute’s $1 Million prize for solutions to P=NP and other open mathematics questions)

The gig has been up for some time…

Much of old school mathematics (and logic)  may be inconsistent with the modern demands of posing the question. The manners in which we have managed to re-ask and formalize the question in modern times suggests both (1) that its resolution is near and (2) the force of habit is strong and any solution may face fierce opposition from those vested in the “old” order of mathematics. For better, worse or other, mathematics as an art form is on its way back.

The question of P=NP may be unraveled in considering the statement implied in the ostensible question, “Does P=NP?”:

As my instructors know annoyingly well, I have at (most) times been lacking in the “show your work” department.

“I got better!”

Still, with a nod to tradition and the interests emphasized by attorneys near and far, I’ll give here only an outline. The rigorous and symbol-laden “proof” showing mathematics in bed with the sultry likes of

“correlation means causality”

and

*wolf whistle* “that which is immediately obvious to the most casual observer is true” is long, geekilicious, and ratherconveniently withheld pending completion of peer review.

Spoilers:

• References to quantum mechanics & associated theory included
• Widely accepted axioms are cast in a curious light (who questions the suitability of Identity or Reflexivity? I might. Others might.)
• Semantics has its day (or at least its 15 minutes)

The problem of resolving P=NP is the very problem of acknowledging and communicating discrepency between representation and the kinds of reality we’re more welcome to discuss in polite company these days, thanks to pioneering research in quantum mechanics. The writeup serves as a brief pedigree of modern mathematics theory, and may manage to invite mathematical and physical fringe theory and modern sociolinguistics into the throne of more classical logic and mathematics.

(This is a rushed post. It has been gathering dust as a Draft for …”some time”; business willing, I may return to update or flush it out some)

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Tags: axioms, bivalence, clay mathematics institute, completeness, complexity, complexity theory, fermat's last theorem, logic, math, mathematics, P=NP, prize money, quantum computing, quantum logic, set theory, sociolinguistics

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