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.
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.