There are two sorts of knowledge in Arcadia: the knowledge of love and academic knowledge. These two types of knowledge are in constant conflict throughout the text. It is only the proposition of marriage, the intellectual justification for sex, which allows a resolution between the two forces. The theme of love vs. intellect is touched upon in the first pages of the play. Thomasina interrupts her lesson with Septimus by asking what carnal knowledge is. Sexual knowledge always acts in conflict with intellectual knowledge, and here it gets in the way of the lesson. Thomasina also remarks on the conflict between emotion and intellect in her history lesson. Her question is prompted by Septimus himself who was found having sex with Mrs. Chater in the gazebo the day before. Thomasina describes Cleopatra as making "noodles of our sex" because Cleopatra was weakened by love. Thomasina heralds Queen Elizabeth who would not have been tempted by love to give away land or power. The great Hannah Jarvis is, like Thomasina's Queen Elizabeth, unswayed by romantic passions. She believes, as does Thomasina, that romantic inclinations would destroy or distract her from her work. Hannah refuses warmth or emotion: she refuses a kiss, denies Bernard's propositions, laughs at Valentine's proposal, and brushes off Gus's flirtation.
Nonetheless, Hannah, like Thomasina, Septimus, and Gus all waltz at the conclusion of the play. Hannah cannot refuse emotion or the bashful Gus by the end of the play and is drawn into an uncomfortable and uneasy dance. The conflict between emotion and intellect is resolved because Hannah suddenly understands that the two are inseparable. Hannah is unlike Thomasina, who unconsciously understands this, driven forcefully by the mystery of both.
Sex remains the final mystery of Arcadia. Septimus, in the conclusion of the play, reveals the final sadness and emptiness of an academic life: "When we have found all the mysteries and lost all the meaning, we will be alone, on an empty shore." Septimus implies that the mysteries of mathematics will someday be solved. As if knowing his own fate, Septimus embraces and kisses Thomasina in earnest, finally indulging in the mystery of his attraction and love. Septimus will not go to Thomasina's room, although she asks him, but he is restrained for a reason that remains unknown. Septimus realizes the ultimately unfulfilling nature of academic progress but will only tragically experience the fulfilling nature of love for a brief moment in a waltz and kiss with Thomasina. In the same manner, Hannah Jarvis submits to a dance with Gus. She, like Septimus, has solved her mystery and now looks to Gus for fulfillment and new mysteries.
Septimus describes to Thomasina the path of knowledge, a humanity that drops knowledge and learning as it picks up new ideas and developments. Septimus tells Thomasina she should not be upset at the loss of the library of Alexandria because such discoveries will be had again, in another time and possibly in another language. This story is ironic to the fate of Thomasina's own discoveries that aren't unearthed until 1993 by Valentine. Thomasina's discoveries are made again: chaos theory and thermodynamics are formal concepts by the time her primer is found and analyzed. Arcadia works as a description of humanity's own progression of knowledge. While Thomasina and Septimus make new discoveries, Hannah and Valentine work to find their discoveries. The work of Thomasina and Septimus is lost but later found again.