The OP has: > The million-dollar question posed by P vs. NP is this: Are these two classes of problems one and the same? Which is to say, could the problems

The OP has: > The million-dollar question posed by P vs. NP is this: Are these two classes of problems one and the same? Which is to say, could the problems that seem so difficult in fact be solved with an algorithm in a reasonable amount of time, if only the right, devilishly fast algorithm could be found? If so, many hard problems are suddenly solvable. And their algorithmic solutions could bring about societal changes of utopian proportions—in medicine and engineering and economics, biology and ecology, neuroscience and social science, industry, the arts, even politics and beyond. Okay, I'd like to have a list of such problems! Yes, some of them are 'intractable', but not all. But we are not attacking the problems that are solvable easily enough now and that would "bring about societal changes of utopian proportions—in medicine and engineering". We are not solving such problems because too few of them exist, that is, mostly the problems don't exist. Here's what we can do now and have been able to do easily enough for decades: The challenge of P versus NP is for (1) exactly optimal (for optimization problems) solutions to (2) worst case problems in (3) polynomial time. But if we will settle for 99+% of the savings of optimal solutions for problems that are not worst case but still constitute nearly all the practical problems in reality, then usually we can do well. E.g., 0-1 integer linear programming problems are in NP-complete. The last such problem I attacked had 40,000 constraints and 600,000 variables. I found a feasible solution within 0.025% of optimality in 900 seconds on a single processor computer using ordinary linear programming and some non-linear duality theory. Blunt, practical fact: In practice, there just are not many practical NP complete optimization problems that people want solved. For practical NP-complete optimization problems, we can usually do well, save nearly all the money to be saved with an optimal solution, for reasonable effort, but, in practice, we don't do that very often because there are not many people with such problems who want such solutions -- for the savings, they just don't care enough even to pick up a phone. The claim that an algorithm that shows that P = NP would "bring about societal changes of utopian proportions—in medicine and engineering ..." is just not true -- the economy does not have many such problems. If the problems were there, then people would be successfully attacking those problems now; the "utopian proportions" would create some recruiting. But the recruiting is not there. Over decades sending many hundreds of resume copies showing such problem solving abilities yields no responses. A person good at such optimization faces deep and profound unemployment -- they just CANNOT be hired, at any price, are just NOT wanted. Quite literally, they would have a better career, e.g., make more money, with a simple, ordinary grass mowing service -- no joke or exaggeration. For the problem with 40,000 constraints and 600,000 variables, I got that via email from two guys, a CEO and his buddy. The buddy had tried simulated annealing, run for days, and quit without knowing how close the results were to optimality. Getting the problem via email, in two weeks I did the non-linear duality derivations and wrote and ran the software, for free. Via email I sent the news of success back to the CEO. He was totally not interested: My success would have embarrassed his buddy, and that meant that my work was not wanted, even for $1. Blunt fact: Not many people have any interest at all, and of those nearly all have very little interest. Point: The claim "bring about societal changes of utopian proportions—in medicine and engineering ..." is nonsense because the needed people with the problems are far too few.