"I thought I'd check up on you. Why aren't you in bed?"
Robert says this to his daughter in the opening scene of the play. While we later realize that this manifestation of Robert is a figment of Catherine's imagination, it shows us the affection and mutually concern in their relationship.
"Yeah. It was just connecting the dots. Some nights I could connect three of four. Some nights they'd be really far apart, I'd have no idea how to get to the next one, if there was a next one."
Catherine says this to Hal in the final scene of the play. She tells him about how she managed to write out the astounding proof he found in the desk. It is an explanation for her work habits, but it also speaks to her approach to life, her sense of uncertainty and the leaps of faith constantly demanded.
"I think you are too."
Hal says this in response to Catherine saying that she thinks she is like her father. She believes she is mentally ill like her father, but Hal's response has to do with his belief that she is a mathematical genius. While Catherine is focused on the negative parallels between herself and her father, Hal focuses on what was good about the man.
"I want to spend the day with you if possible. I'd like to spend as much time with you as I can unless of course I'm coming on way too strong right now and scaring you in which case I'll begin backpedaling immediately."
Hal says this the morning after he sleeps with Catherine. The line shows that Hal is a charming if somewhat awkward guy, who says what he is thinking and doesn't mind embarrassing himself a little bit. It is an endearing line, because it shows that he is honest and affectionate towards Catherine.
“Let X equal the quantity of all quantities of X. Let X equal the cold. It is cold in December. The months of cold equal November through February. There are four months of cold, and four of heat, leaving four months of indeterminate temperature. In February it snows. In March the Lake is a lake of ice. In September the students come back and the bookstores are full. Let X equal the month of full bookstores. The number of books approaches infinity as the number of months of cold approaches four. I will never be as cold now as I will in the future. The future of cold is infinite. The future of heat is the future of cold. The bookstores are infinite and so are never full except in September...”
In a flashback, Robert tells Catherine that he feels like he is making strides with his work, and asks her to read some of it. When she does, this is what she finds, a chain of nonsensical statements. It is devastating to Catherine, because she thought he was getting better, but this writing proves that he is still unwell.
"I know...it works...But all I can see are the compromises, the approximations, places where it's stitched together. It's lumpy. Dad's stuff was way more elegant."
At the end of the play, Hal wants to look at the proof with Catherine, but she tells him that she is dissatisfied with it, comparing her own work to that of her father. Even though she knows her proof is "correct," she wants to find a better way to write it.
"I would like to see a doctor called Doctor Von Heimlich: Please find one. And I would like him to wear a monocle. And I'd like him to have a very soft, very well-upholstered couch, so that I'll be perfectly comfortable while I'm blaming everything on you."
While it seemed like Catherine is more than willing to go with Claire to New York, here she reveals that she is feeling much saltier about it than it had appeared. She sarcastically makes ridiculous requests of Claire, and insinuates that if she starts going to therapy, she will only blame all of her problems on her sister.
"It makes my hair feel, look, and smell good. That's the extent of my information about it. You might like it if you decide to use it."
Claire says this to Catherine on the eve of their father's funeral, after recommending a shampoo to Claire. Claire is very different than Catherine, in that she takes pleasure in the finer things, and is much more practical than her abstract, intellectual sister.
"After my mother died it was just me here. I tried to keep him happy no matter what idiotic project he was doing."
In this moment, Catherine confides to her new acquaintance Hal about how much she took care of her father. All alone, she indulged her father's ideas, no matter how insane or delusional they were.
"Oh they're raging geeks. But they're geeks who, you know, can dress themselves...hold down a job at a major university...Some of them have switched from glasses to contacts. They play sports, they play in a band, they get laid surprisingly often, so in that snese they sort of make you question the whole set of terms—geek, nerd, wonk, dweeb, Dilbert, paste-eater."
Hal tries to make a case for the appeal of the modern math geek, describing some friends of his who are in a band and who, in spite of their predisposition towards geekiness, are actually pretty cool guys. In the course of this monologue, it becomes clear to Catherine that Hal is talking about himself as much as he is about his "friends."
