Beauty Bare

 Millay's poem takes a reductionist view of beauty: "Beauty bare" refers to the idea of pure geometric beauty, unfettered by art, emotion, and other human creations. Euclid, the original great geometer, dealt with the geometric concepts by themselves, and so, argues the poet, saw a more natural and clearer view of the essence of beauty. Others, who claim to have seen beauty, simply "ponder on themselves" and stare "at nothing, intricately drawn nowhere in shapes of shifting lineage." In other words, what they are seeing is clouded by subjectivity and cultural heritage, and is therefore not as close to the true nature of beauty. They see approximations to the real thing, which Euclid alone was able to see.

Kramer's poem makes fun of this opinion, mostly by pointing out that it's a little silly to say that only a single person has ever seen "beauty bare". Interestingly, this is a mathematician's rebuttal to math elitism, ridiculing the idea that poets and musicians (Orpheus, in this case) do not have as much a claim to beauty as Euclid does. I agree with his assessment; we don't get to decide that mathematical beauty is beauty in its purest form, since in doing so, we cheapen the other human artistic pursuits.