| Quote #1
She felt, at the same time, a growing respect for the adversary, for a science that was so clean, so strict, so luminously rational. Studying mathematics, she felt, quite simply and at once, "How great that men have done this." (188.8.131.52)
Dagny's love of math crops up often in the book; it represents her worldview, which favors reason over emotion. The language used to describe mathematics here is interesting: adversary, clean, strict, rational. These are terms that apply both to Dagny herself and to things she admires (like a good challenge).
| Quote #2
"Let's find out" was the motive he gave to Dagny and Eddie for anything he undertook, or "Let's make it." These were his only forms of enjoyment. (184.108.40.206)
Francisco is the embodiment of an engineer here, taking joy in discovering, making, and doing. Engineers are celebrated throughout the novel, and it's no accident that Dagny herself studied engineering.
| Quote #3
They spoke of the [Rearden] metal and of the possibilities which they could not exhaust. It was as if they were standing on a mountain top, seeing a limitless plain below and roads open in all directions. But they merely spoke of mathematical figures, of weights, of pressures, resistances, costs. (220.127.116.11)
Rearden Metal symbolizes the achievements of people who share Galt's values. It also serves as a sort of symbolic "victim" in the struggle with the looters, who continually try to steal and misuse it. Rearden Metal also adds to the book's alternate universe/science fiction-y feel. The "merely" is used somewhat ironically here, since, in this book's value system, things like science and math and money are considered very worthy topics of conversation.