Septimus is a romantic.  He believes in the existence of genius and finds beauty in that belief.  He sees life as an adventure to discover and experience all the secrets of the universe -- secrets of the flesh, secrets of the mind, secrets of the heart. 
As the play continues, however, he loses his idealism.  Life at the Croon Estate continues to bring him complications and disappoints.  He becomes bitter about the realities of the world.  This is symbolized in his slow acceptance of Thomasina's mathematical experiment.  He realizes Thomasina is right, and her theory suggests the eventual end of the universe. What he mourns, however, is not the end of life but the loss of innocence. "When we have found all the mysteries and lost all the meaning, we will be alone, on an empty shore,’’ he laments before joining Thomasina in her first, and last, waltz.