From Thomasina's opening question about carnal knowledge and Septimus's clever answer considering the question we are interested. Who is that young girl? Who is that handsome young man?
Thomasina is an amazing young girl with an incredible mind. It doesn't take us long to understand this. It doesn't take long for Septimus to discover this either. He recognises that she is a prodigy.
Thomasina has a crush on her handsom and charming tutor. She wouldn't be the first girl to fall in love with her teacher.
We see Thomasina as precocious. She may only be a young girl but she has the mind of a woman. She enjoys teasing Septimus.
In today's vernacular, Septimus is a player. Because he is more intelligent and clever than the people he is playing, it is fun to watch him manipulate everybody.
His feelings for his young protege are sincere. Even if Thomasina had lived, there would have been no possibility of them being together. They lived in a class society. Septimus was of the wrong class.
Their dance together is one of the most beautiful moments in the play.
For Septimus, his life without Thomasina was empty and he spent the rest of his life working on her theory. Now, that was love.