By setting much of Arcadia in 1809, Stoppard contrasts two distinct historical periods: the Enlightenment and Romanticism. The Enlightenment of the eighteenth century emphasized structured, logical thinking, adherence to established rules, and drew inspiration from Classical Greek and Roman ideals of simplicity, proportion, and controlled emotion in culture, art, and literature. In contrast, the Romanticism of the early nineteenth century was a conscious rebellion against Enlightenment principles. Romantic thinkers and artists experimented with literary forms, emphasizing individuality, freedom, and the untamed beauty of nature in their works.

The characters in Arcadia, both in the historical and modern scenes, embody these contrasting philosophies. Lady Croom is intent on preserving her gardens, which are influenced by classical ideals, noting, "The slopes are green and gentle. The trees are companionably grouped at intervals that show them to advantage. The rill is a serpentine ribbon unwound from the lake peaceably contained by meadows on which the right amount of sheep are tastefully arranged." Her opponent in matters of taste is the landscape architect Richard Noakes, employed by the unseen Lord Croom, who is eager to transform the meticulously maintained gardens into a Gothic wilderness, featuring a waterfall, dark forest, and charming hermitage. He justifies his approach by simply stating, "It is the modern style."

The conflict between Lady Croom and Noakes over Sidley Park's gardens mirrors some of the play's more abstract themes. In the modern scenes, Bernard Nightingale and Valentine Coverly embody the conflict between intellect and emotion. Bernard relies on intuition and emotion, pursuing the improbable theory that Lord Byron fled England in 1809 after killing a minor poet in a duel. He clings to his belief despite evidence to the contrary, driven by "Gut instinct. The part of you which doesn't reason. The certainty for which there is no back-reference."

Valentine, in contrast, is an Oxford graduate student researching chaos theory, seeking patterns in the fluctuation of numbers in his family's ancient hunting records. To him, Bernard's pursuits seem insignificant. "The questions you're asking don't matter, you see," he tells the conceited professor, "It's like arguing who got there first with the calculus. The English say Newton, the Germans say Leibnitz. But it doesn't matter. Personalities. What matters is the calculus. Scientific progress. Knowledge."

Ultimately, each participant gains insight into the other's perspective. Bernard hastily moves to publish and promote his theory without having all the necessary information, only to be publicly humiliated when he realizes he was entirely mistaken. A bit more thorough analysis and less reliance on instincts would have benefited him greatly. Meanwhile, Valentine must acknowledge the presence of genius—a human drive that transcends scientific explanation—when he delves into Thomasina's lesson book and discovers she had conceptualized a theory of chaos long before it was recognized by scientists.

A genius is an individual with innate talents, characterized by exceptional intelligence or creativity. Their perceptive abilities might be extensive, covering various fields of study and art, or they might excel in a specific domain such as writing, mathematics, or communication. In Arcadia, some characters are labeled as geniuses, while others fervently strive to achieve that status. Some individuals even question the existence of genius, much like they doubt fate or a higher power.

Thomasina Coverly is likely a genius. At the age of thirteen, she seeks to prove Fermat's Last Theorem and attempts to create a numerical formula to describe the shape of a leaf. She perceives things others do not and can intellectually challenge anyone at Sidley Park. When she asks her tutor, Septimus, if she is more clever than her elders, he responds: "Yes. Much." Septimus believes that...