On the film Proof

Catherine has to prove herself as well as proving mathematical theory. Which is Catherine’s greatest
struggle, proving her sanity to Claire or her mathematical ability to Hal? Which “burden of proof” is
actually a burden?
While Catherine is a devoted daughter and Claire is trying to be a good sister, there is never any mention
of their mother, Robert’s wife. Create a reason why she is never mentioned and never appears onstage.
Explain if Catherine or Claire demonstrates the greater need for control, what motivates their need for
control and how do they express that need?