It is difficult for me to fully understand these two poems as the use of symbols and metaphors can have different interpretations. I will try my best to show my understandings in this blog.
In Millay’s poem, she admired Euclid’s achievement in seeing the “beauty bare” which I guess can be interpreted as the axioms he concluded. She emphasized that Euclid saw these all by himself and the others only happen to know the surface of the beauty of mathematics. In contrast, Kramer doubted Millay’s statement that Euclid alone established the foundation of mathematics. I agree with his opinion since instead of being the creator of the book The Elements, Euclid was more like an editor. He studied in Plato's Academy and got inspiration from other mathematicians such as Hippocrates of Chios, Eudoxus and Theaetetus. I would say Euclid stood on giants’ shoulders and thus he had a chance to generalize and organize previous knowledge in math and contributed more to the field.
In addition, there are some discussions about whether Euclid was a historical character or it represented a group of Greek mathematicians at Alexandria. Here is one link I found interesting. https://mathshistory.st-andrews.ac.uk/Biographies/Euclid/
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