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- Since Thomasina is still quite young, her research isn't performed within a professional setting. Being in certain respects a genius, she can more clearly grasp these abstract ideas about the nature of the universe, physics, algebra, etc.
She posits certain ideas that she derives from the concepts that she is exploring with Septimus -- particularly algebra
"If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future; and although nobody can be so clever as to do it, the formula must exist just as if one could." (Scene 1)
Yes. (Pause.) Yes, as far as I know, you are the first person to have thought of this. (Pause. With an effort.) In the margin of his copy of Arithmetical Fermat wrote that he had discovered a wonderful proof of his theorem but, the margin being too narrow for his purpose, did not have room to write it down.
"What a faint-heart! [...] We will start with something simple. (She picks up the apple leaf.) I will plot this leaf and deduce its equation. You will be famous for being my tutor when Lord Byron is dead and forgotten." (Scene 3)
Thomasina: You did not like my discovery?
Septimus: A fancy is not a discovery.
- Her research and the way she conducts it are closely tied to her desire to be seen as equal as well as her own intellectual curiosities that she pursues on her own time
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