When I pick up a pen to write on a particular subject, often it is useful me to try to follow a pattern for rhymes or syllable-counts -- for the effort to conform to a pattern challenges me to think about my topic in new ways. In the history of poetry, rhyme-choices were frequent--yielding sonnets, villanelles and a variety of other forms.
In recent years, online and printed versions of poems have become very accessible and the principle, "Rhymes help us remember" has become less of a focus in poetry. One of the popular connections between math and poetry has been the use of Fibonacci numbers to choose syllable counts; especially popular has been the FIB, a six-line stanza in which the syllable-counts are 1, 1, 2, 3, 5, and 8 -- the first six Fibonacci numbers. (Inventor of the FIB was Greg Pincus, and lots of information is provided here in this 2010 blog posting, Poems with Fibonacci number patterns.)