When Aylmer announces to Georgiana that he plans to remove her birthmark, he concludes his lengthy speech with an allusion to the character Pygmalion:
...what will be my triumph when I shall have corrected what Nature left imperfect in her fairest work! Even Pygmalion, when his sculptured woman assumed life, felt not greater ecstasy than mine will be.
In Greek mythology, most notably in Ovid's Metamorphoses, Pygmalion is a sculptor who falls in love with one of his statues. Nearly a century after Hawthorne wrote "The Birthmark," George Bernard Shaw borrowed the character for his play Pygmalion, in which Professor Henry Higgins transforms an awkward girl into a refined lady and likewise falls in love. In both cases, a man of art or intellect transforms the object of his attentions into a woman worthy of love.
Given the timeline, we know that Hawthorne drew inspiration from Greek mythology. But why did he choose this particular allusion? Perhaps he strove to imbue his own story with the power, potency, and wide readership of epic poetry. Aylmer represents the sculptor, and Georgiana represents the statue. But this allusion also calls attention to Hawthorne's ironic reversal of the original Pygmalion story. Pygmalion creates a statue more perfect than any living woman but wishes that she were human. Aylmer sees his wife's potential for perfection and sacrifices her life in his efforts to attain it. Ovid's story ends euphorically, with the two lovers looking into each other's eyes. Hawthorne's ends with Georgiana's death.
Another interesting aspect of this allusion is that it appears in dialogue. Aylmer himself chooses to compares his situation to a fictional one. At first, the juxtaposition seems to suffuse his lofty thoughts with the power of old poetry. But upon further examination, it rather foreshadows the impossibility of his aspirations. Note also the moment's dramatic irony, as Aylmer remains unaware of the consequences of his project and continues to believe that his success will succeed Pygmalion's until the final pages show otherwise. The reader, however, is aware from the narrator's frequent foreshadowing that Georgiana will in all likelihood die, and thus might react to this moment with a knowing chuckle or troubled frown.