The play is set in one location, a large room in an English country house in Derbyshire. The scenes shift back and forth in time. The first scene takes place in April 1809.

Thomasina Coverly, a 13-year-old student, and her tutor, the 22-year-old Septimus Hodge, are working on two separate problems. Thomasina is occupied with a math problem while Septimus is reading a book of poetry. In the midst of her studying, Thomasina abruptly asks Septimus what “carnal embrace” (1) is. Initially, Septimus lies, stating it is hugging beef. He uses his knowledge of linguistics to fabricate the origins of the phrase.

Septimus asks how Thomasina’s math problem is coming. She is struggling to find a proof for Fermat’s last theorem, which Septimus reveals is an unsolved proof from 1637. Septimus is reading a poetry collection by Mr. Chater, a guest at the house.

Thomasina and Septimus discuss the household gossip that inspired Thomasina’s question about carnal embraces. She describes how she heard Jellaby telling the cook that Mrs. Chater was discovered in the gazebo in a carnal embrace. This news worries Septimus, and he pushes for more information, as it is later revealed that he is the man she was with.