Theorem-proof / Cut-up / poems

     For mathematicians, reading a well-crafted proof that turns toward its conclusion with elegance and perhaps surprise -- this mirrors an encounter with poetry.  But can one have that poetry-math experience without being fluent in the language of mathematics?  Below I offer a proof (a version of Euclid's proof of the infinitude of primes) and a "cut-up" produced from that proof-- and I invite readers (both mathematical and non-mathematical) to consider them as poems.