One simple way to determine whether you are among the "incompetent who are not aware of their incompetence" might be to ask yourself: do you have unanswered questions about the topic?
The competent tend to answer "yes" and can quickly reel off many hard, deep, unanswered questions.
Incompetent Person: I feel competent in asserting that 2 + 2 equals 4.
Reasonably Competent Mathematician: What exactly do I mean by "two"? By "plus"? By "equals"? Sure, 2+2 equals 4, but is the answer unique? Why? What real world scenario is 2+2 being applied to? Why is it safe to map these abstract concepts of numbers and arithmetic to concrete objects or situations in the real world?
Incompetent Person: These questions have never occurred to me, or these questions bore me.
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