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You say, “The ‘mathematical poem,’ if it is to be, or to contain, poetry, must have some poetic elements, as well as some formal symbols and operations of math.”
I don’t understand why you have, “if it is to be, or to contain, poetry.” If you call it a poem, claim I, you are saying that it is a poem, so much have poetic elements, however defined. That such a poem should have “some formal symbols and operations of math,” follows from its being called a “mathematical poem.” Ergo, I would rephrase your definition as “A mathematical poem is a poem containing mathematical elements.”
I would then ask you to say what you mean by “having” mathematical operations in a mathematical poem. That is, would a poem about a child who has to do five long division problems for homework “have” a mathematical operation in it?
Also, to be fastidious, I would want you to spell out whether the symbols and operations should be overtly in the poem. Some, as you probably know, seem to think a sonnet is a mathematical poem because the poet has to be able to count up to 14 to make one.
Which leads to the next important thing I think needs to be done: sort out all the kinds of math-related poems it seems reasonable to distinguish from one another. I would list the following five:
(1) poems that discuss math
(2) poems generated by mathematical operations.
(3) poems that use mathematical symbols but use them unmathematically: e.g., a poem with a square root sign next to the word “Sunday,” which is followed by seven plus-signs, whereupon the poem becomes standard verbal expression.
(4) poems that one or more persons claim arouse some kind of “mathematical feeling.”
(5) poems that perform one or more mathematical operation central to its aesthetic meaning.