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malcolmocean 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.
So in that case, the question is in some ways addressed by narrowing the meaning of "field".
If a physicist interprets Hamming's question as "what is the most important problem in your field?" as "what is the most important problem in physics?" then obviously not everyone should be answering it. If, instead, the physicist interprets it as "what is the most important problem in quantum cryptography?", that being his/her more specific field, then it becomes more reasonable (and more vital!) that the physicist is indeed working on the most important problem in their field.
Although, upon reflection, if I decide to become the world's expert in lit-match juggling, and the most important problem is lighting the third one before the first two burn down, that is obviously not necessarily an important problem on a larger scale. But I think my point above still has value even if it's missing something that permits this counterexample.