I agree with your basic point, but i think it's not about theory vs. the real world so much as confusing the worst case for the practical case. I often think

I agree with your basic point, but i think it's not about theory vs. the real world so much as confusing the worst case for the practical case. I often think that approximation algorithms, randomization algorithms, fixed-parameter tractability and "special case" deterministic algorithms are what people should look at if they are interested in positive solutions (as opposed to lower bounds). Not to mention the incredible success of SAT solvers.