Suppose an intelligent lay person is ignorant of mathematics and believes all the crap taught in classrooms to the effect that mathematics consists of believing dogmas, obeying instructions, and executing algorithms. Suppose this person works in some capacity recognizable as professional and is in other respects literate and professional. Certainly there are many such people.
What mathematics problems might this person encounter and fail to recognize as mathematics problems? (Realistic examples, but not necessarily frequently seen examples.)