Maybe not now. But there's a sense in which that should be expected. Here's the situation:
There are some biggie problems out there having to do with combinations of discrete things, optimization with such things, etc. For example, this challenge led to the question P versus NP. Bluntly, there is a big supply of potentially tasty nuts there we are unable to crack or poor at cracking.
If want to crack those nuts, e.g., have something "useful", then likely we have to back off on a direct attack via some one bright idea, technique, paper, and chunk of code. Instead, we have to, say, build a foundation, circle around the problem and look for entering wedges, construct some tools, look for related, seeming somewhat promising smaller results that in time we could build on to make progress to the real goal of being good at cracking those tasty nuts.
So, right, maybe we are not sure yet that some result will be useful -- that's sad but just part of the challenge of cracking those nuts. They are tasty but tough nuts to crack. Moreover, such results are about the best we see; we should take, and take seriously, the best we do see.
So, that's part of how research works, for much of the best we know how to do, in pure and applied math. Yes, I know; I know; they don't always make this aspect of research fully clear in freshman calculus!!!
I agree. It is wrong to wag fingers saying impractical etc. Lower bound theory is about adversaries against _all possible algorithms_, not just the analysis of a given algorithm. So progress is expected to be slow.
George Polya in his book "How To Solve It?" encourages to think about "What is the easiest problem that you cannot solve yet?" Most theoretical results tend to answer this, and this principle is a good guideline for theoretical research.
There are some biggie problems out there having to do with combinations of discrete things, optimization with such things, etc. For example, this challenge led to the question P versus NP. Bluntly, there is a big supply of potentially tasty nuts there we are unable to crack or poor at cracking.
If want to crack those nuts, e.g., have something "useful", then likely we have to back off on a direct attack via some one bright idea, technique, paper, and chunk of code. Instead, we have to, say, build a foundation, circle around the problem and look for entering wedges, construct some tools, look for related, seeming somewhat promising smaller results that in time we could build on to make progress to the real goal of being good at cracking those tasty nuts.
So, right, maybe we are not sure yet that some result will be useful -- that's sad but just part of the challenge of cracking those nuts. They are tasty but tough nuts to crack. Moreover, such results are about the best we see; we should take, and take seriously, the best we do see.
So, that's part of how research works, for much of the best we know how to do, in pure and applied math. Yes, I know; I know; they don't always make this aspect of research fully clear in freshman calculus!!!