“Maybe the world was like a revolving door, it occurred to him as his consciousness was fading away. And which section you ended up in was just a matter of where your foot happened to fall...And there was no logical continuity from one section to another. And it was because of this lack of logical continuity that choices really didn't mean very much.”

“Once you pass a certain age, life becomes nothing more than a process of continual loss. Things that are important to your life begin to slip out of your grasp, one after another, like a come losing teeth. And the only things that come to take their place are worthless imitations. Your physical strength, your hopes, your dreams, your ideals, your convictions, all meaning, or then again, the people you love: one by one, they fade away. Some announce their departure before they leave, while others just disappear all of a sudden without warning one day. And once you lose them you can never get them back. Your search for replacements never goes well. It’s all very painful – as painful as actually being cut with a knife.”

“When I was little, I had this science book. There was a section on 'What would happen to the world if there was no friction?' Answer: 'Everything on earth would fly into space from the centrifugal force of revolution.' That was my mood.”

“Principles and logic didn't give birth to reality. Reality came first, and the principles and logic followed.”

“But still," Ayumi said, "it seems to me that this world has a serious shortage of both logic and kindness.""You may be right," Aomame said, "But it's too late to trade it in for another one.”

“Math is like water. It has a lot of difficult theories, of course, but its basic logic is very simple. Just as water flows from high to low over the shortest possible distance, figures can only flow in one direction. You just have to keep your eye on them for the route to reveal itself. That’s all it takes. You don’t have to do a thing. Just concentrate your attention and keep your eyes open, and the figures make everything clear to you. In this whole, wide world, the only thing that treats me so kindly is math.”

“I don't know -- maybe the world has two different kinds of people, and for one kind the world is this completely logical, rice pudding place, and for the other it's all hit-or-miss macaroni gratin.”