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).
"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.
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.
"A man with the genius of a great scientist, who chose to be a commercial inventor? I find it outrageous. He wanted a motor, and he quietly performed a major revolution in the science of energy, just as a means to an end, and he didn't bother to publish his findings, but went right on making his motor. Why did he waste his mind on practical appliances?"
"Perhaps because he liked living on this earth," she said involuntarily. (18.104.22.168)
Stadler reveals his own biases here when he fails to appreciate the value of technology. He only believes in pure science and fails to understand the need to use it for practical ends. Dagny's remark emphasizes how she links life to positive actions.
"Hank, that motor was the most valuable thing inside this factory," she said, her voice low. "It was more valuable than the whole factory and everything it ever contained. Yet it was passed up and left in the refuse. It was the one thing nobody found worth the trouble of taking." (22.214.171.124-162)
The motor plays an important role in symbolizing the strike and the strikers' values, and helps reveal the blindness and ignorance of society at large, who dismiss it as junk.
"Point Four. No new devices, inventions, products, or goods of any nature whatsoever, no now on the market, shall be produced, invented, manufactured or sold after the date of this directive." (126.96.36.199)
The disastrous Directive targets business and science as the "enemy." Science is all about discovery, and change, which is of course what looters like James find terrifying.
"Our first rule here, Miss Taggart," he answered, "is that one must always see for oneself." (188.8.131.52)
Galt, and Akston later on, express a sort of Scientific Method view of life, emphasizing the need to gather evidence for oneself before making a judgments or forming hypotheses.
The farmhouse tore into strips of clapboard and went down, followed by a geyser of the bricks of its chimney..... It was so swift, so uncontested, so simple, that Dr. Stadler felt no horror, he felt nothing, it was not the reality he had known, it was the realm of a child's nightmare where material objects could be dissolved by means of a single malevolent wish. (184.108.40.206)
Project X is like something out of a science fiction nightmare. Stadler seems to want to deny its connection with science, comparing its effects to an evil wish or a nightmare. He doesn't want to acknowledge the evil that science can be used to perpetrate.
Dr. Stadler leaped to stop him – but Meigs shoved him aside with one arm, gave a gulp of laughter at the sight of Stadler falling to the floor, and with the other arm, yanked a lever of the Xylophone.
The crash of sound – the screeching crash of ripped metal and of pressures colliding on conflicting circuits, the sound of a monster turning upon itself – was heard only inside the structure. No sound was heard outside. (220.127.116.11-91)
The destruction of Project X is a very fitting symbolic end to the looters' regime, as is the fact that Meigs is the one to pull the lever. An ignorant thug, Meigs rose to power in a criminal regime and then brought down destruction on everyone by abusing the "tools" of the looters' system.
"That's what you think!" said Ferris, and chuckled. "You haven't seen our experimental model in action. Last month, we got three confessions in three unsolved murder cases."
"If . . ." started Mr. Thompson, and his voice cracked suddenly into a moan, "if he dies, we all perish!"
"Don't worry," said Ferris. "He won't. The Ferris Persuader is safely calculated against that possibility." (18.104.22.168-28)
It's also fitting that the looters would use science and technology to develop machines for torture and exploitation.