Euclid Poems

Image source: https://history-biography.com/euclid/

 Euclid's collection of different works in "Elements" has had a major influence on mathematics and different scientific fields since it was written. In particular, the geometrical principles influenced physics, astronomy, chemistry, some engineering (https://history-biography.com/euclid/). I believe the poem by Edna St. Vincent Millay is praising Euclid's understanding and appreciation for geometry. My interpretation is that the "Beauty" referenced in this poem is referring to geometry in particular because of the lines, "intricately drawn nowhere/ In shapes of shifting lineage." I think "intricately drawn nowhere" refers to the abstraction of common shapes and patterns found in nature but documented mathematically in "Elements," while I think "In shapes of shifting lineage," is a reference to the work of others ("lineage") that Euclid collected. Thus if "Beauty" is geometry and "Euclid alone has looked on Beauty bare," then the poet claims that Euclid is the only one who was experienced enough to see geometry in all of its glory. The lines "Let all who prate of Beauty hold their peace,\And lay them prone upon the earth and cease\To ponder on themselves," further perpetuates the idea that no one else is close to Euclid's understanding of geometry and those who speak of it aren't qualified to. The line, "Fortunate they\Who, though once only and then but far away,\Have heard her massive sandal set on stone," tries to convey how far away everyone else is from Euclid's connection to geometry by saying it is rare for people even to have "heard [Beauty's] massive sandal set on stone." 

In contrast, I believe the parody poem by David Kramer criticizes the idea that Euclid alone held a superior understanding and appreciation of geometry. I believe he is saying that many have achieved greatness in geometry, even if it was only a very specific section, when he says, "Has no one else of her seen hide or hair?/Nor heard her massive sandal set on stone?/Nor spoken with her on the telephone?" Then by addressing the poets and saying "For Beauty bare you never yet had seen," I believe the Kramer is saying both that the poets were unqualified to speak on the matter and that Euclid was a starting point but definitely not the be-all end-all of the field of geometry. It's almost as though Kramer expresses that Euclid couldn't have been so special to have been the only one allowed access to geometry when he says, "Would you, for this mathematician, \Remove...Once only, and then but far away, your sandal?" Thus, I think the first poem is expressing that very few brilliant minds besides the great Euclid have been fortunate enough to really grasp geometry in its entirety, while the second one rejects this idea and instead implies that geometry is accessible to everyone.