When is theoretical computer science useful?
In class, we learned about the halting problem, Turing machines, reductions, etc. A lot of classmates are saying these are all abstract and useless concepts, and there's no real point in knowing them (i.e., you can forget them once the course is over and not lose anything).
Why is theory useful? Do you ever use it in your day-to-day coding?
Answer
True story:
When I got my first programming job out of graduate school, the guys that owned the company that I worked for were pilots. A few weeks after I was hired, one of them asked me this question:
There are 106 airports in Arkansas. Could you write a program that would find the shortest rout necessary to land at each one of them?
I seriously thought he was quizzing me on my knowledge of the Traveling Salesman Problem and NP-Completeness. But it turns out he wasn't. He didn't know anything about it. He really wanted a program that would find the shortest path. He was surprised when I explained that there were 106-factorial solutions and finding the best one was a well-known computationally intractable problem.
So that's one example.