The poet and the geometer

Even in a short poem, [the] structure undergoes transformation. The poet may select only the crucial changes and never note the principle, but if the poem is successful it records the intellectual rhythm along with the verbal choreography. In longer poems and in semipoetic literature, such as the drama and the novel, there is always an element, often called character, leitmotif, or idea, undergoing a development. Amid this change, it stands or becomes increasingly rigid and, for some readers and writers, substantial and real…I think the comparison of mathematics and poetry is illuminating on this point, for this is one of the places where a poem and a geometrical demonstration meet. A demonstration, as we shall see, uncovers a figure in transformation just as a poem reveals a character in action. The demonstration tries to be literal; this quality is sometimes called accuracy and exactness. The poem tries to be adequate; its quality is sometimes called imagination and associative eloquence. I shall not ask the question here how far each succeeds.

—Scott Buchanan, Poetry and Mathematics