In the early 1990s I began to gather examples of poetry with mathematical imagery to enrich my mathematics classes at Bloomsburg University. Both poetry and mathematics employ concentrated language, stating with concise elegance more than is first apparent. Gradually I became a writer of poems and, within this activity, have looked for mathematical influences on the structure of poetry. Drawing on examples from these past explorations, I develop and illustrate these points: (1) mathematics and poetry demand similar creativities; (2) constraints involving mathematics give poets the opportunity to discover new language; (3) mathematics offers precise and vivid imagery for poems.