• The only time in the book that Ishigami expresses any true emotion is when he cries out in anguish in the last scene. Yasuko visits him in jail, sorrowful and apologetic about being the cause of so much suffering. Her confession to the police means that she will likely be charged with murder as well, which means that all of Ishigami’s careful planning will have been been in vain. His grief and anguish testifies to his love for her, and one wonders whether he would’ve been better off simply applying his keen mathematical mind to winning her love the old-fashioned way, taking her on a date, buying her a ring, and going through the usual courtship procedures that human beings have employed since time immemorial. Nonetheless, it is a poignant and well-executed ending, perfect in all its tragic connotations.

• Suicide features prominently in this chapter, especially in connection with the role of fate and free will. It is Misato’s attempted suicide that clinches Yasuko’s decision to confess, as she was weighing the possibility of marrying Kudo and moving on with life. Yusako does not have the luxury of being able to decide whether to confess her crime or run off with Kudo – Misato’s attempted to suicde forces her to act on the basis of conscience. The pure innocence and love of a child overcomes her attempts to rationalize away the guilt she might have felt over marrying Kudo. It’s always been intense human emotions that have represented the confounding variable that give rise to the unanticipated turns of events that impede the progress of his carefully laid-out plans. Ironically, it was the irrational infatuation that he felt for Yasuko that saved him from attempted suicide. It is overwhelming human emotion that saves him, and it is overwhelming human emotion that results in his demise. All the mathematical precision in the world cannot anticipate the fateful events that come about without regard to mathematical necessity, such as that of Yusako and Misato appearing on the day of his attempted suicde. When he wishes to die, Ishigami is saved by Misato and Yusako. When he wishes to save Yusako and Misato, Misato almost ends up dying and Yusako ends up being charged with murder. Despite people’s best intentions, fate has a way of using people’s plans against them and enforcing its own will on the universe.

• Given Ishigami's gratitude to Yasuko for saving him just as he was at the point of death, it is hard to see past his double standard towards the "Engineer," the homeless man who, like him, was full of hopelessness and despair. One would think that Ishigami's salvation experience would have given him an appreciation for life and enabled him to feel empathy for others who are in circumstances similar to him, especially someone so mathematically inclined as the "Engineer." Ishigami's callousness towards the "Engineer" certainly diminshes one's opinion of him, since one can't help speculate on how happy the "Engineer" must have felt about Ishigami offering him a job. It may very well have been the kind of life-changing event that would have saved the "Engineer" from destitution and possibly suicide, and yet Ishigami had to turn it into a perverse mockery of the salvation that Ishigami himself had the privilege of experiencing.

• Another major theme in the novel is that of the nobility of unrequited love, quite common in Japanese literature and philosophy, and exemplified in the following quote:

“He held no aspirations of ever being anything to them. He knew he should never even attempt to make contact. It was like his relationship with mathematics.: it was enough merely to be associated with something so sublime. To seek any kind of acknowledgment would sully its dignity.”

• The desire to be with someone while secretly yearning for them is often more fulfilling than actually being with that person. While yearning for someone, we cling to an idealized image of the object of our affections. As soon as he attain the object of our affections, however, we become disappointed by the mundane reality of it and grow weary of its ordinariness. It ceases to possess the allure that aroused our desire in the first place. Such is the concept of the nobility of unrequited love, and it is this sentiment that is expressed in the quote above, a quote that is made all the more tragic when we consider how Yasuko, reflecting upon how unworthy she is of Ishigami’s sacrifice, diminshes herself as nothing more than a middle-aged woman with no charm.

• Finally, the tragic ending evokes a strong feeling of mono no aware, which goes hand in hand with genuine tragedy. As readers, we feel sad about the how Yasuko and Ishigami will ultimately end up being charged with murder and separated from each other. As the same time, there is a certain satisfacion in seeing Ishigami for once express something approaching genuine human emotion, since he's been mostly obssessed with logic and calculation up until this time, showing only a blank expression betraying no hint of genuine human feeling. There is also satisfaciton in seeing Yusako finally able to appreciate what Ishigami has done for her and finally able to realize the extent of Ishigami's love for her. We could only speculate on how things might've turned out differently if only circumstances were different, but such is life.