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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.)

Michael Hardy
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  • What about that a layperson likes some musical piece? I'm thinking of something like Bolero being created by following some structure as first principle... – C-star-W-star Jul 19 '14 at 02:45
  • I think it's easier to establish what problems AREN'T mathematics problems – Silynn Jul 19 '14 at 03:25
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    @Silynn : If it is easier, that doesn't mean it is as informative. – Michael Hardy Jul 19 '14 at 03:28
  • " Identify the key parameters and formulate formal definitions of them." This is taken from the middle of a Keith Devlin essay on "What is mathematical thinking?" Part of the theme of this essay is that there are mathematics problems that mathematicians fail to recognize as mathematics problems but are able to solve because of "mathematical thinking" rather than any specific mathematical knowledge. http://devlinsangle.blogspot.com.au/2012/08/what-is-mathematical-thinking.html – Gerry Myerson Jul 19 '14 at 04:25
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    Curiosity trumps intelligence in recognizing the importance of mathematics. Curious lay persons are likely to arrive rather quickly at existence issues (i.e. there exists a Rabbit Hole named math, and the Hole goes very deep indeed beyond 1,2 and 3) just by asking a few questions, even if they can't understand all (or even a small fraction of) the details. Incurious but intelligent lay persons ignore the Hole altogether. – user_of_math Jul 19 '14 at 06:27
  • There are problems with which mathematics can help, like "dividing up rent among a group of people", but given a precise phrasing of the corresponding mathematical problem, I think it would sound much more like mathematics. Would things like that count? – Mark S. Jul 19 '14 at 15:45

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