The play opens with the problem (quite literally) of mathematical knowledge. Septimus has given Thomasina the challenge of finding a proof for Fermat's Last Theorem (more to keep her occupied than in hopes of her solving it). At the time the play was written Fermat's Last Theorem was, indeed, a great mathematical task. Thomasina proposes her own original solution to the theorem: Fermat's marginal note was an eternally tormenting joke to drive posterity mad. It is ironic that in real life, shortly after the play opened, Andrew Wiles announced a proof of Fermat's theorem that has, after subsequent amendments, been accepted as correct. But the quest for mathematical knowledge persists within the play. Thomasina is the genius girl who can miraculously understand the foundations of thermodynamics and chaos theory a century before their formal definition.
Thomasina's algebra lesson is interrupted by her own search for another type of knowledge. Thomasina asks Septimus what "carnal embrace" is. Septimus's characteristically witty reply, that it is the act of throwing one's arms around a side of beef, does not deter Thomasina from her desire to know about sex. Chloe, Thomasina's modern counterpart, has less desire for formal, mathematical, or book knowledge but craves sexual knowledge. For Thomasina, the desire for sexual knowledge is a juvenile curiosity&emdash more a means to marriage and a first waltz. On the other hand, for the modern hormonal Chloe, sex is real sex; Chloe persuades Bernard to go up into the library stacks with her for what may be real sex. Until Thomasina is sixteen, she only desires the waltz and kiss. While Thomasina asks Septimus to come to her room after they waltz in the conclusion of the book, he refuses, and she is content.
Thomasina studies history with disdain and boredom. As she tells Septimus, she is bored with and hates Cleopatra. Thomasina abhors Cleopatra's weakness for men and sex, as she complains Cleopatra makes "noodles of our sex." Thomasina has seemingly distinguished between sex that is exciting and sex that weakens women and destroys knowledge and progress. Thomasina, herself, seeks sexual knowledge and mathematical knowledge but does not sacrifice one for the other. Historical knowledge is also sought after more urgently in the present. In scenes depicting modern-day Sidley Park, historical knowledge is rewarded by great fame and possibly sexual prowess. The modern characters value historical knowledge foremost. Bernard, of course, lusts after historical knowledge most of all, intent on receiving any and all fame it may bring. Hannah, with more reserve, also looks among the books of Sidley Park for a glimpse into the past and writes bestsellers on her findings.
The intertwining past and present of Sidley Park provides commentary on the progression of knowledge or quest for knowledge in modern times. The modern day characters are concerned with the workings and findings of the past, while Thomasina and Septimus work to make new discoveries. The quest of all of the scholars thus forms a sort of loop; what is undervalued in one generation is greatly revered in the next. The state of inquiry revolves and evolves from an interest in the future to that of the past. And, like Septimus's apt description of humanity's quest for knowledge, the modern day continues to pick up what has been lost in the past, while simultaneously finding new ideas and formulas.