The standards of proof are different from the fundamental operation of "OK, cool, you solved this problem. Why does this problem matter? Isn't it useless? Senseless? Meaningless?" You have this same question whether or not you're in an a priori discipline (mathematics), scientific fields proper, or engineering. "Absolute certainty" has nothing to do with it. I can assure you, people on the job are not looking for The Absolute Truth when doing their jobs, yet they still can question at a solution by asking: are we solving the right problem?

(Although in general, there's no true difference between "I answered the question correctly, but the question was mapped to this thing we call 'reality' wrong", and "I answered the question incorrectly", because you can (try) adding the constraints that you really wanted targeted in case A, to case B, and boom, suddenly a question/answer pair that was "Answered correctly, but question doesn't map to reality" now becomes, "You answered this question wrong". However, individuals generally tend to have some breakpoint to differentiate between the two).

No, what I'm saying is that I don't agree that taste in mathematics is more uniform than taste in coding! Mathematicians argue about taste all the time. Just as you might look at a piece of code and agree that it compiles and doesn't have any fatal bugs but still think it's badly written, hard to follow, hard to modify, or whatever else, mathematicians judge mathematical work using very similar criteria.