No doubt you have studied the sheer irony of this short story, about a woman whose secret turns out to be that she does not have a secret at all. The very thing Lady Alroy uses to attract a man, ends up driving him away in the end.
The themes of this story follow the satirical irony. It is a story that speaks a message about the sheer irony of love and relationships, and perhaps the so-called "laws of attraction." At first meeting, Lady Alroy certainly intends to portray herself as a woman of mystery. Her reasons for doing this are left ambiguous, which is likely a comment on one of the nuances of women that men don't understand. What is clear, however, is that her mysteriousness is exactly what attracts Gerald (and possibly other men) to her. This seems to be the goal.
It does not seem like Wilde's purpose for this story was to solve this particular mystery of women. Instead, he simply intends to point out the irrationality of women who seek to succeed in the game of attraction, and when they do, refuse to participate in the resulting relationship. No matter what, these women are destructive. The story suggests that the thrill of the chase will always end in disappointment, because whether it ends in success (catching the man) or not, the chase must end.
In "The Sphinx Without a Secret," Wilde explores the theme of love. This is shown from the beginning of the story when the narrator meets with his friend Lord Murchison, a man who is "troubled" by his amorous feelings for Lady Alroy. It is interesting to note that Murchison's love for Alroy is based primarily on physical attraction and, in drawing attention to this, Wilde argues that love is as much about beauty as any other, deeper factor. Moreover, it is Murchison's love that drives the plot of the story: his "troubled feelings," for example, and his desire to marry Lady Alroy provide the story's interest.
Secondly, Wilde also considers the theme of mystery. Specifically, he explores the question of why mystery is so attractive and intriguing. This is shown through the character of Lady Alroy and the many mysteries of her life, like her appearance in the yellow brougham, her different address, and her secret lodgings. Moreover, by never revealing the truth about Lady Alroy and her many secrets, Wilde keeps the reader guessing to the very end, without ever explaining the truth.