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Jiro comments on Privileging the Question - Less Wrong
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The correct response to Hamming's question is "Because I have a comparative advantage in working on the problem I am working on". There are many, many important problems in the world of greater and lesser degrees of importance. There are many, many people working on them, even within one field. It does not make sense for everyone to attack the same most important problem, if indeed such a single problem could even be identified. There is a point of diminishing returns. 100 chemists working on the most important problem in chemistry are not going to advance chemistry as much as 10 chemists working on the most important problem, and 90 working on a variety of other, lesser problems.
This point was first made to me by Richard Stallman who told me quite clearly that free software was not the most important problem in the world--I think he cited overpopulation as an example of a more serious problem--but software freedom was the problem he was uniquely well situated to address.
There are seven billion people in the world. I know of no problem that actually needs 7 billion minds to solve it. We are pretty much all well advised to find the biggest problem we have a comparative advantage at, and work on solving that problem. We don't all have to, indeed we shouldn't, all work on the same thing.
And a response that brings up another important point is simply that everyday language is said without precision. When someone claims that their problem isn't important, they don't mean that it has zero importance, and when they say it's not going to lead to something important, they aren't really claiming that it has a zero chance of leading to anything important. Indeed, they aren't even claiming aht the expected value of it is low--imagine they are working on something which, by contributing to general knowledge, increases the odds of solving each of 2000 problems by 0.1% each, Nobody in their right mind would claim that that is an important problem, yet it increases the expected number of important problems that are solved by more than 1.