Donna Masini, one of my poetry teachers at Hunter College, offered this rule of thumb for use of a particular word in a poem: the word should serve the poem in (at least) two ways -- in meaning and sound, or sound and motion, or motion and image, or . .. .
Richard Wilbur (1921 - ) is a former US Poet Laureate (1987-88), a prolific translator, and one of my favorite poets -- and perhaps this is because he seems to maximize his word-choices with multiple uses. When I read Wilbur, I see and hear and feel -- and, after multiple readings, these sensory impressions coalesce into understanding. Here is one of his sonnets, a poem of the geometry of absence:
In Trackless Woods by Richard Wilbur
In trackless woods, it puzzled me to find
Four great rock maples seemingly aligned,
As if they had been set out in a row
Before some house a century ago,
To edge the property and lend some shade.
I looked to see if ancient wheels had made
Old ruts to which the trees ran parallel,
But there were none, so far as I could tell—
There'd been no roadway. Nor could I find the square
Depression of a cellar anywhere,
And so I tramped on further, to survey
Amazing patterns in a hornbeam spray
Or spirals in a pine cone, under trees
Not subject to our stiff geometries.
"In Trackless Woods" is found in Richard Wilbur's Collected Poems, 1943-2004 (Houghton Mifflin Harcourt, 2004).
Multiple meanings of terms is not obligatory in mathematics as Masini suggested it should be for poetry. BUT it frequently happens: mathematics, like poetry, forms connections and patterns. Indeed, the student who likes and knows mathematics fluently switches from one meaning to another. The symbol "2" denotes an integer or a rational number or a real number or a complex number. A real number is a point on a line or an infinite decimal or a convergent Cauchy sequence or a Dedekind cut. A function is a rule or a formula or a set of ordered pairs or a graph or ... . And so it goes.