1. Why is it strange that Catherine and Robert are speaking in the beginning of the first scene?
It is strange because Robert is dead: he passed away a week before.
2. What does Robert reveal about Catherine's state of mind in the first scene?
Not only is she talking to a dead person, but she mopes around the house and sometimes does not get out of bed all day. It appears she is depressed, or has some mental health issue.
3. Why is Hal insistent on going through all of Robert's notebooks?
He feels it is his duty as a professional to make sure none of the notebooks has important mathematics in them. Also, Robert was his mentor, and he feels he must got through them as a personal tribute to the man.
4. Robert was a graphomaniac. What does that mean?
Graphomania is a condition when one compulsively writes. Often, the writing is completely incoherent, or gibberish.
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