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In Scene 1, which takes place in 1809, Thomasina, a 13-year-old British aristocrat, learns the definition of “carnal embrace” from her tutor Septimus. Meanwhile Noakes, the landscape gardener for the estate, has discovered Septimus making love with Mrs. Chater, a houseguest, in the gazebo. The cuckolded Mr. Chater wants to duel Septimus, as was the custom, for the offense to his wife. Septimus deflects Chater’s rage by complimenting his terrible book-length poem, “The Couch of Eros,” and hinting that he’ll give Chater a positive review. Lady Croom enters, with Noakes and Brice, to discuss and complain about Noakes’s planned changes to the garden. Noakes plans to replace its pastoral elegance with a Romantic-style wilderness.

In Scene 2, which zooms forward to the present day, Bernard, a scholar of the Romantic era, arrives at Sidley Park. He meets Hannah, another academic who is already there, studying the garden and the Sidley hermit, who she thinks symbolizes Romanticism. Bernard professes to be interested in Chater’s poetry, having found a copy of “The Couch of Eros,” but Hannah uncovers him for who he really is—a Byron obsessive who’d written a mean review of her previous book. Despite Hannah’s dislike of him, Bernard decides to stay around Sidley Park to do research. He thinks he may have found evidence that Byron was a houseguest at the same time as Chater, and that they dueled, with Byron killing Chater. We also meet the modern-day Coverly siblings, the current residents of Sidney Park, Valentine, Chloë, and Gus.

In Scene 3, back in 1809, Thomasina impatiently tries to read Latin. She picks up her math instead, proclaiming her intention to find an equation that will express the form of an apple leaf. Thomasina mourns the loss of ancient literature because of the fire at the library of Alexandria, and Septimus gives a stirring speech about the inherent good of the human search for knowledge. Brice and Chater return, with Chater newly offended to have discovered that Septimus wrote a scathing review of his previous book. Chater again wants to duel, and now Septimus consents.

In Scene 4, in the present day, Valentine and Hannah look over Thomasina’s old math notebook, in which Thomasina wrote a note about how she’s discovered a way to describe nature with math. Valentine figures out that Thomasina was making patterns using iteration, a very modern technique that he himself uses in his doctoral research to try to find patterns in the local grouse population. Bernard enters, still focused on proving that Byron killed Chater in a duel. After he and Hannah discuss some pieces of evidence, with Hannah remaining skeptical about Bernard’s hypothesis, Valentine reveals that Byron definitely stayed as a guest at Sidley Park, because his hunting was recorded in a game book. Bernard runs off in astonishment to find the game books.

In Scene 5, Bernard begins to read his paper about Chater and Byron to the family. The siblings and Hannah interrupt many times, and Valentine points out that Bernard didn’t include the statistical data that go against his hypothesis. Bernard, offended by the challenge to his big idea, makes an impassioned case that poetry is more important than science, and Valentine storms out. Bernard invites Hannah to London “for sex,” but she dismisses the idea. Bernard leaves, and Hannah reads Valentine some new information from a 19th-century article about the hermit—the hermit was obsessed with mathematical ideas about the fate of the universe which sound suspiciously like Thomasina’s.

In Scene 6, in the past, Septimus enters the house in the early morning. He learns from the butler, Jellaby, that Chater, Mrs. Chater, Brice, and Byron all left early in the morning, because Lady Croom found Mrs. Chater with Byron. The implication is that Lady Croom was having an affair with Byron, and she didn’t like finding another woman with him. Because of the sudden departures, Septimus never had to fight his duel with Chater, which would have been that morning. The day before, Septimus, expecting to die, had left a love letter for Lady Croom, and now she invites him to her sitting room.

In Scene 7, past and present overlap. Chloë and Bernard discuss Bernard’s paper and sex, Chloë’s favorite topic. Hannah and Valentine sit together to work on the hermit project and the grouse project, respectively. Valentine shows Hannah a computer-expanded version of Thomasina’s algorithm. The discovery would have made Thomasina famous, Valentine thinks. Hannah explains that Thomasina died in a fire right before her 17th birthday. In the past, which is superimposed on the present, Septimus and Thomasina, now 16 and about to turn 17, talk about geometry and Thomasina’s algorithm. Thomasina draws a sketch of Septimus with his tortoise. Hannah, reading Lady Croom’s garden book, finds out that Chater discovered the dahlia, which disproves Bernard’s whole theory. Bernard gets upset. In both time periods, the characters prepare for evening parties. Septimus finally understands Thomasina’s algorithm, while Valentine finally realizes Thomasina's genius. Chloë’s mother discovers Chloe and Bernard carrying on, and Bernard abruptly leaves Sidley Park. Thomasina gets Septimus to teach her how to waltz. Gus brings Hannah the drawing of Septimus and the tortoise that proves he was the hermit, and Gus and Hannah dance side-by-side with Thomasina and Septimus.